Rochester Institute of Technology RIT Scholar Works

Theses

8-1-1984

A signal-to-noise ratio analysis of an autoradiographic image enhancement process

Donald R. Williams

Follow this and additional works at: https://scholarworks.rit.edu/theses

Recommended Citation Williams, Donald R., "A signal-to-noise ratio analysis of an autoradiographic image enhancement process" (1984). Thesis. Rochester Institute of Technology. Accessed from

This Thesis is brought to you for free and open access by RIT Scholar Works. It has been accepted for inclusion in Theses by an authorized administrator of RIT Scholar Works. For more information, please contact [email protected]. A SIGNAL-TO-NOISE RATIO ANALYSIS OF AN AUTORADIOGRAPHIC IMAGE ENHANCEMENT PROCESS

by

Donald R. Williams A.A .S. ROCHESTER INSTITUTE OF TECHNOLOGY (1978)

A thesis submitted in partial fulfillment of the requirements for the degree of Master of SCfence in the School of Photographic Arts and Sciences in the College of Graphic Arts and Photography of the Rochester Institute of Technology August , 1984

Donald R. Williams Signature of the Author _ . Photographic Science and Instrumentation Division

Ronald Francis Accepted by . Coordinator, M.S . Degree Program

I College of Graphic Arts and Photography Rochester Institute of Technology Rochester, New York

CERTIfICATE Of APPROVAL

M.S. DEGREE THESIS

The M.S. Degree Thesis of Donald R. Williams has been examined and approved by the thesis committee as satisfactory for the thesis requirement for the Master of Science degree

Edward M. Grahger Dr . Edward M. Grahger. Thesis Advisor

John Carson Mr. John Carson

James Jakubowski Mr. James Jakubowski

Date

;i A SIGNAL-TO-NOISE RATIO ANALYSIS OF AN AUTORADIOGRAPHIC IMAGE ENHANCEMENT PROCESS

by

Donald R. Williams

Submitted to the Photographic Science and Instrumentation Division in partial fulfillment of the requirements for the Master of Science degree at the Rochester Institute of Technology

ABSTRACT

A signal-to-noise ratio(SNR) analysis of a S-35 thiourea autoradiographic image enhancement process incorporating subproportional bleaches is performed, with emphasis on diagnostic medical Imagery. Quantifying SNR through a spatial frequency definition of DQE and NEQ, these metrics were compared between donor and receiver-composite stages. While improvements in radiometric speed and gamma were noted in the receiver-composite, these gains were more thanXffset in a SNR sense by correspondingly lower MTF and higher

Wiener spectrum values. As a result the donor's DQF^^ of .30 exceeded that of the receiver-composite's by 50%. DQEmavImCXA Similarly, exceeded that of the receiver composite's 350%. the donor's NEQ av by max . The donor's DQE and NEQ continued to exceed that of the receiver-composite even on an equi -exposure basis.

TV ACKNOWLEDGEMENTS

The author wishes to thank the following for both technical and facility support in the completion of this thesis:

Dr. E.M. Granger, Mr. John Carson, 4 Mr. James Jakubowski for both technical support, and in their capacity as thesis committee members.

Mr. Phillip Bundh and his colleagues at the Kodak Research Laboratories, Rochester,N.Y..

Xerox Corp., Webster, N.Y., for microdensitometer and computer facility access.

Dr. Plewes and Dr- Owunwanne of Strong Memorial Hospital, University of Rochester, Rochester, N.Y. and Mr. Roland Porth for use of the MTF computer programs. TABLE OF CONTENTS

Page

INTRODUCTION 1

1 . 1 Autoradi ography 2

1.2 Signal Detection and Signal to Noise Ratio 4

1.3 Statement of the Problem 13 EXPERIMENTAL 16

2.1 Image System Definition 17

2 . 2 Samp! e Generati on 22

2.2.1 Donor and Receiver Photographic Materials 24

2.2.2 Donor Screen/Film Exposure and Sensitometry 24 2.2.3 Chemical Processing 25 2.2.4 Receiver Film Exposure 26

2.3 Data Capture and Processing 26

2.3.1 Densitometry- macro 4 micro 27

2.3.2 Characteristic Curve Data Acquisition 28 2.3.3 Characteristic Curve Data Processing 28 2.3.4 MTF Data Acquisition 29 2.3.5 MTF Data Processing 30 2.3.6 Wiener Spectra Data Acquisition 32 2.3.7 Wiener Spectra Data Processing 32 RESULTS 35

3 . 1 Characteristic Curves 36

3.2 Modulation Transfer Function 38

3.3 Wi ener Spectra 39

3.4 DQE and NEQ 41

3.5 DQE and NEQ Error Analysis 42

DISCUSSION 55 56 4 . 1 Characteristic Curves

4.2 Modulation Transfer Function 59

4.3 Wiener Spectra 61

4.4 DQE and NEQ 67

4.5 Applications of DQE and NEQ 72

CONCLUSIONS 77

vi 6. REFERENCES 87

7. APPENDICES 89

7.1 Appendix A - Equipment, Processing, 4 Measurement Parameters 90

7.2 Appendix B - Calculations 4 Curve Fits 96

7.3 Appendix C - Supplemental Graphs 106

7.4 Appendix D - Computer Programs 128

8. VITA 139

vn LIST OF FIGURES

Figure # Page

1 X-Ray exposure scenario 18

2 Image chain block diagram 21

3 Experimental procedure block diagram 23 4 Characteristic curves for donor 4 receiver-comp 45 5 Gamma vs. log exposure curves 46

6 MTFs for donor and receiver-comp 47

7 Wiener spectra for donor 4 receiver-comp @ 0=1.0 48 8 Wiener spectrum for donor vs. log exp. 4 frequency 49 9 Wiener spectrum for rec.-comp. vs. log exp. 4 frequency 50

10 Equi -frequency Wiener spectrum values vs. log exposure 51

11 Equi -frequency Wiener spectra with characteristic curves 52 12 Donor DQE and NEQ vs. log exposure 53 13 Receiver-comp. DQE and NEQ vs. log exposure 54 14 Receiver-comp: donor gamma ratio vs. log exposure 58

15 MTF comparisons to reference 38 60

16 Rossman's Wiener spectrum model 62 2 17 MTF 4 Wiener spectra comparisons 64

18 Wiener spectra @ .4 vs. density 65

19 Receiver-comp. : donor DQE ratio vs. log exposure 69 20 Donor DQE and receiver-comp. NEQ comparison vs. log exp 74

21 Image chain block diagram 81

22 Characteristic curves for donor 4 receiver-comp 82

23 MTFs for donor and receiver-comp 83

24 MTF comparisons to reference 38 83

spectra with 25 Equi -frequency Wiener characteristic curves 84

26 Donor DQE and NEQ vs. log exposure 85 27 Receiver-comp. DQE and NEQ vs log exposure 86

vm 1. INTRODUCTION 1.1 Autoradiography

As photography evolved from an art to a science, a natural consequence was the evaluation and extension of the photographic image as an information medium. This spawned a plethora of techniques to enhance the photographic image

Information beyond what was considered to be normal. Even to this day new techniques continue to be proposed. However, only a handful of these methods survived the gauntlet of practicality and success.

One of these processes which, at first, did not appear especially appealing from an image enhancement perspective was a

1 * 2 radiation emission method . Over the years this method has come to be known as autoradiography. Basically, the procedure involves toning the original silver 1mage(the donor) with a radioactive material. When the toned image was placed 1n contact with another unexposed silver halide material (the receiver), the decay properties of the radioactive material led to a subsequent latent image in the receiver. Since the amount of toner and with it radiation emissiond.e., exposure) is proportional to the amount of silver at a given location, wherever there was a high density in the donor there was a proportional amount of latent image or, after development, density. Likewise, low donor densities led to low receiver densities. Therefore, upon development, the receiver was a duplicate positive Image of the donor.

While this method was originally intended as a duplication scheme, It eventually found a use as an image 3 enhancement method . The Idea behind the enhancement 1s to radioactively tag the donor's image silver that does not contribute significantly to the optical density yet does contain image information. Most of this information 1s In the toe region of the characteristic curve and is associated with individual Image grains rather than a large number of grains. By radioactively tagging this silver one hopes that the information in this region will manifest itself 1n the receiver, and in turn increase the photographic speed. The feasability of recent efforts using this scheme has suffered however due to inherent radiation hazards, equipment considerations and unacceptable image quality.4.

Be that as it may, one process that has shown considerable promise and seems to circumvent some of the above mentioned problems is an autoradiographic image Intensification method developed by Askins . Similar to the radiation emission method, the original silver image of the donor 1s reacted with

Askins' radioactive nuclides. For s process these are beta-particle emitting nuclides and because of their low energy tend to optimize the enhanced image's resolution. These nuclides take the form of thiourea S-35 in an activating or toner bath. Once the donor has been bathed in this activating bath It

1s dried, and one then has a radioactive Image whose radioactive flux at any location is proportional to the amount of silver at that point. This radiotoned film is then placed 1n contact for a given duration of time with another silver halide emulsion, the receiver, and subsequently developed as one would a normal Image from silver halide materials.

The chemical mechanism behind the procedure can best be o described through work done by James and Vanselow . It is believed that the silver ion reacts with the thiourea through the thione

OH" RCNH2=S presence of ion the yielding Ag+. In the , following reaction occurs:

^C=S*-Ag+ + OH"-*- HN = C-S-Ag + HgO (1).

H2N

However, at higher pH the silver thiourea compound reacts via the equation: f ? Ag+? OH" = + = HN C-S-Ag + -#- Ag,S + RC N + H,0 (2),

With respect to Askin's process, any silver existing in the donor material 1s aerially oxidized to Ag+. This oxidized silver is then reacted with the radioactive S-35 to form silver sulphide as outlined in equation 2. In essence, the silver image in the donor has been radioactivated. The difference between this and classical two stage Imaging systems though 1s the fact that the silver 1n the first stage no longer acts to stop radiation but rather to create it.

Previous and existing work with this process in the field of medical radiography has led to reports of Increases in speed, visual detection, and resolution 1n the receiver Image when

' ' compared to the donor image. However, one of the major problems in the receiver images has been the high fog levels. This is a direct result of the non-selective nature of the chemical reactions in distinguishing between image and non-image silver. In an effort to diminish these fog levels Vachon and Wheaton studied the effects of subproportional reducers at various stages of the processing and achieved encouraging results from a signal-to-noise ratio viewpoint.

The attributes of the receiver Image that were encouraging were not only the speed increases, but also the increased characteristic curve gammas and lower fog levels. These latter two are of keen Interest from a signal detection viewpoint.

To see how they figure Into signal detection a signal -to-noise ratio (SNR) analysis is appropriate. The necessary background for this analysis follows.

1.2 Signal Detection and Signal -to-Noise Ratio

A film's sensitivity or speed has typically been of primary concern in the evaluation and development of photographic materials. To be sure, optimizing a film's speed Is a desirable parameter in many applications. Unfortunately, it alone tells the

user nothing about the signal detection capabilities of the film.

More than anything, it only informs the user of how well the film will act as a density meter. The point to be made 1s that speed by itself is of little concern when trying to detect faint stars in

distant galaxies, or to distinguish tumors or cancerous cells in

the human body. One may be using the fastest film available on the market, but it will be of limited utility If upon processing one is

unable to discern signals on it because of the inherent noise in

the film.

With this in mind, one may question the relative merits

of different systems of speed measurements when in many practical

cases one is interested in not only speed but also signal

detection. Thus, a marriage of the two parameters would seem in order rather than treating them seperately. The latter may have 13 still been the case had it not been for Rose and his Introduction

of the concept of efficiency. Important subsequent work on this 14 15 16 and various concept was performed by Jones , Fellgett , Shaw , 17 18 19 ' * other workers . To understand how the concept of efficiency

evolved and its relation to speed and signal detection, it would be

helpful to first understand the parameters that affect a detector's

ability to distinguish any given signal.

A signal 1n the photographic sense manifests itself as a

change in density against some uniform background density. The

strength of this signal will of course determine how well it is

detected. However, in most detection problems the strength of the

signal 1s minimal, and as Implied above, the real limiting factor

becomes the amount of noise that corrupts the signal. Noise in this fluctuations. case, can be quantified by the root-mean-square(rms)

From a thermodynamic point of view, the least amount of noise that

one can expect from an Ideal radiation detector would be that due

to the photon noise of the incident radiation. Assuming that this radiation is governed by Poisson statistics, the photon noise associated with an Ideal detector working at some mean exposure level, q, is/q .The signal -to-noise ratio ( SNR ) for the perfect detector then becomes:

SNRin= ~J=-=J* )

"in" The subscript implies input. It is imperative to recognize at this point that the signal and noise are referred to in the exposure domain. The need for this becomes evident shortly.

From purely heuristic arguments, one measure of how well a system will perform would be to compare the noise associated with

the ideal detector as defined above with that of a detector at hand. In a sense one is not faulting the system under evaluation for noise that was introduced by the incident photons. This measure of the signal detecting efficiency has been termed the Comparative 20 Noise Ratio. Other equivalent terms found in the literature for this measure are Detective Quantum Efficiency(DQE), Equivalent Quantum Efficiency (EQE), and Detective Efficiency. For the sake of convention, DQE will be adopted throughout this paper. The working equation for quantifying DQE experimentally can be developed by knowing the way in which the output and input noise characteristics are related relative to the same criteria.

For photographic films, output fluctuations are made relative to density, whereas measurements of the input noise are made relative to exposure. As mentioned above, to compare these noise levels on an equal basis, it is necessary to make use of the characteristic ( D-Log q) curve.

It is well known that

dD dD q y=. = (4) d( log q ) dq log-^e where Differential gamma along the D-log q curve D Optical density

Average quantum exposure per unit area

If the mean square fluctuations in density,

G - Cl (5)

where C^> is the rms density fluctuations as measured with an aperture of area A, and G is a constant referred to as Selwyn's constant. These density fluctuations are related to an equivalent

A,Aq* number of quantum fluctuations within an area by equation

4. Mathematically, this relation is

G 2 dq 2 Aq tf =

^ tOVT G-A( TJ ! og10e

2 In other words, Aq is a measure of the output fluctuations as UU tL measured with an aperture area A, expressed in terms of an equivalent number of input quanta. The assumption being made in equation 6 that allows us to do this is that the measured output

fluctuations

Aq2 - q = qA (7) in in

Therefore, by comparing the input fluctuations as defined in equation 7 with the output fluctuations in equation 6, the ratio between the two, - thus the term, comparative noise ratio - or DQE becomes:

* ( 1o9lOe } ' DQE = (8) G-q

Through equation 8 it becomes constructive to recognize

alternate interpretations of DQE. By noticing that 1/q is a speed measure and that G is a granularity measure, one common

interpretation of DQE has become a speed-to-granularity ratio. It

seems logical that for a given speed film, signal detection would be inversely related to the granularity. Generally, this is the case.

A more intuitive feel for DQE can be gained by recalling

from equation 3,

SNRin = -~^r- -yq

or

(SNR.n)2 = q (9)

By defining the output SNR in equivalent exposure terms as 2 Signal {a"W* 1 f ab;; Equiv. Noisel G-( ) L -1 dD

One finds that

nog10e)2 (10)

(SNR.n): G-q

The result of course is identical to the expression for DQE in equation 8. Therefore, one finds that

(SNRout}' DQE = (11)

(SHR1n)'

Insight Into the principle of DQE 1s best reflected through equation 11. The SNR . will always deteriorate relative to the SNR..n, since occurances to the contrary would violate laws of statistical entropy. The exception, of course, exists for an ideal detector where the above SNR's are equal.

Also, since an efficiency of any kind can usually be described as some ratio, Rose's concept of efficiency finally becomes more evident from equation 11. To develop this idea thoroughly, we know that

(SNRout>' DQE = (S"W

(SNR.n>< 10

In order to maintain the integrity of the above equation we may define 2 2

Q' (SNRollt)2 - = JE ll out (12)

or

q'

DQE =

By examining equation 12 one may think of the system as

working at some SNR associated with an exposure level q', whereas

if inefficiencies in the system did not exist at all ( I.e. DQE =

100$) the system would be working at some greater SNR associated

with an exposure level q. It is as 1f in attempting to count q ?1 system q' quanta, the was only successful in counting quanta .

q' The exposure value as defined in equation 12 has come

to be known as the Noise Equivalent Quanta(NEQ) per unit Image

area. The utility of NEQ arises from SNR optimization

considerations. While DQE is a measure of SNR per unit energy, NEQ

measures the SNR per unit image area. Therefore, one finds that for

applications where exposure criteria 1s critical ( i.e., the

recording stage ) one would want to base exposure on maximum DQE.

On the other hand, 1f there was no limit to the amount of available

energy ( i.e., the printing stage ) the exposure would be based on maximum NEQ values. It is important to differentiate between these

SNR measures and to determine which Is to be used for the

application at hand.

In an effort to keep a numerical and less abstract

perspective on matters, It may be helpful at this point to realize

some typical DQE and NEQ values of silver halide materials arrived

at through experimentation. Most of these DQE values He within a range of 11-4% at their maximum value. Compared to other detectors like photomultiplier tubes with DQEs approaching 100%, silver 11

halide materials then, are sadly outperformed. There have been various schemes to increase these low values however, that work quite well. Most of them are Implemented at the emulsion design

step and have been studied via the existing models22. The main

factors that lend towards these low values are the

threshhold/saturation nature of the individual receptors(i.e.,

grains), random spatial array and size distribution of the

receptors, variable grain sensitivities, and fog. Typical NEO

values of . silver halide materials lie between .1 and .2 quanta/um

In early experimental work many of the reported DQE values were actually In error. This was due to the overriding

assumption in the previous analysis that the noise parameter as measured on the film, OX is done so with apertures that are large in comparison to the size of the grains. From a frequency analysis

viewpoint then, one is only measuring the fluctuations at low

spatial frequencies since the aperture is prefiltering the higher

ones. For the general case, this aperture dependent DQE then 1s not

desirable. However, this situation was rectified through work 23 performed by Shaw . By describing the input and output fluctuations via the Wiener Spectrum, a more complete frequency

analysis of DQE was described. A synopsis of Shaw's work is derived

below via the equations already defined.

It follows from equation 6 that the output fluctuations

are

^2 )2 j-,2 , A( ? (13) out B -1og10e

In keeping with the more complete frequency analysis, the output 2 replaced with Wiener noise parameter, , is the two dimensional

spectrum of the density fluctuations, arriving at

1 9 )c2 = W(u,v,q)A( CT0 *(u,v,q) (14) out ^-M(u,v)(log10e) 12

= where u, v Rectangular spatial frequency coordinates W(u,v,q)= The two-dimensional Wiener spectrum of the

density fluctuations corresponding to an

exposure level q.

M(u,v) = The two-dimensional Modulation Transfer Function.

It is necessary to introduce M(u,v) into the denominator of equation 14 due to the possibility of the output noise becoming less than the input noise at higher frequencies. Assuming that the input has a flat Wiener spectrum, the Input noise then becomes

2 = (T .,-n(uv) qA

Combining this with equation 14, and assuming an isotropic Imaging system, the spatial frequency definition of DQE becomes

no9,ne)?U(q,)?WTF(),? DQE(w.q) * (15) q.W(w.q)

where w = rotationally symmetric spatial frequency

Through this manner of definition, one finds that DQE 1s no longer dependent on the aperture size and that both a micro- and macroscopic formulation of DQE exist. A complete SNR analysis of a film system can now be achieved by knowing Its D-absolute log q curve, MTF, and Wiener spectrum.

" By using the above analysis, several authors have demonstrated the application of DQE to particular disciplines. One of these areas which plan to be Investigated in this work, medical radiography, has especially benefitted due to the exploding field of medical diagnostic imaging. Knowing the DQE and NEQ 1s genuinely useful 1n this area since one is interested in not only detecting weak signals for maximum exploitation( i.e., NEQ ), but also doing 13

it with a minimum of X-Ray exposure to the patientd.e., DQE). Indeed, this is exactly what DQE and NEQ indicate about a detector! the By knowing exposure for maximum DQE, one can most efficiently detect any given signal. Once this signal 1s detected, It can then

be amplified in the signal to noise sense 1n the second stage

process by knowing the film's NEQ characteristics. Both DQE and NEQ

become important. DQE to detect the signal with as little exposure

as possible, and NEQ to help in the interpretation of that signal

by making its detection highly probable. The two must go

hand-in-hand 1n this application.

1.3 Statenent of the Problen

Through research efforts on the thiourea S-35

autoradiographic process, much has been learned of the macroscopic

image characteristics of the process as 1t applies to medical

radiography. Included in these efforts were evaluations of

resolution and signal detection using tri-bar targets and

9 ' 10 phantoms. It was reported that both resolution and signal

detection increased. Resolution was determined through inspection

of the tri-bar targets and signal detection through evaluation by

medical personnel of the phantom images. Due to the nature of the

evaluation techniques very little Insight was lent as to why these

authors' increases occurred. One only knows that according to the

observations these changes did occur. As suggested previously, one

way of gaining Insight into these changes is through a signal

detection or SNR analysis. Specifically the measurement of DQE and

NEQ for the process in question. Recall that the autoradiographic process employing

subproportlonal bleaches appeared especially appealing from a SNR

viewpoint. In addition to increased speed( 1/q ) and gamma(*tf ) of

the receiver image when compared to that of the donor, the high fog

problem 1n the receiver image was also alleviated. Inspection of equation 7 would then suggest that DQE and NEQ might Increase from 14

donor to receiver Images. The decreased fog would also help 1n extending the latitude DQE and NEQ. Two key measures that would verify this are lacking however: namely the MTF and Wiener spectrum. Qualitatively, one might expect that when generating the second( receiver) Image from the f1rst( donor) Image, the MTF would decrease and the Wiener spectrum values increase. This of course is likely to offset any possible DQE or NEQ gains offered by Increases in gamma and speed. Indeed, the nature of entropy would almost dictate it. If this Is so though, and one accepts SNR as a basic visual detection criteria, how then does one reconcile the reported increases 1n visual detection pointed out earlier?

With these thoughts in mind, The experimental objectives of this research are twofold. They are:

1) Measure the DQE and NEQ of a subproportional bleaching

autoradiographic process with specific emphasis on

medical diagnostic Imagery.

2) Evaluate the results and draw conclusions on the donor

facto" and receiver image processes as "de image systems

based on the DQE and NEQ measurements.

In achieving these objectives, several questions hope to be answered. They are:

1) Is the DQE or NEQ greater 1n the donor or max. max. donor-receiver combination?

2) How do the DQE and NEQ between donor and donor-receiver Images

compare on an equi-exposure basis? and

3) When treated as a two stage expose-to-print process Is the

exposure at maximum DQE in the donor step the same as the

exposure for maximum NEQ in the donor-receiver step? 15

This last question will determine if the two steps truly complement each other from a SNR viewpoint and 1s of certain interest for this intensification process's optimization.

Finally, because of the largely positive results with the autoradiographic process for image intensification, the hypothesis for this research is

"de-facto" Hypothesis: When treated as Imaging systems the receiver imaging process outperforms the donor process in a SNR sense at some point along the

exposure domain.

The way in which these objectives, questions and hypothesis plan to be addressed are outlined in the experimental section that follows.

It is in this section that the definitions of the donor and receiver processes are given along with the method of implementation for data capture and processing. 16

2. EXPERIMENTAL 17

As pointed out earlier, the measurement of DQE and NEQ 1s one of the prime experimental objectives of this work. This being the case, this experimental section bears heavily on the validity and interpretation of the results. For, It 1s here that the measurement foundations are laid. Once this 1s done, the approach

1s defined and the actual work of sample generation and measurement

takes place.

The cornerstone to all of this Is of course defining the actual Image system to be analyzed, followed by a statement of what

parameters of the system need to be measured. All of this is

accomplished in the first section, 2.1, on Image System Definition. Other sections relating to generating the necessary samples and

subsequent methods of data capture and analysis follow.

Occasionally, certain Input/output relationships are referred to throughout this section, however, their exhibition is held for the

results section and the reader 1s asked to be patient. With this as

a background, let us begin.

2.1 Iaage Systea Definition

From the Introduction, It should be clear that two

entities of the autoradiographic process, namely the donor and

receiver steps, need defining before any measurement work can be

performed. Furthermore, they must be defined within the context of

an operational medical Imaging environment. Therefore, a short

scanario of this environment might prove helpful.

Classical medical Imaging 1s always done by means of an

X-ray flux passing through some medium. The structure of this medium (i.e. bone, muscle, etc.) differentially attenuates the flux and therefore gives rise to a potential image. Next, some way of

necessary. 1s detecting and recording this image becomes This film cassette placed but 1n accomplished by means of a beyond,

object imaged. Figure 1 Illustrates close proximity to, the being 18

POINT SOUKCE

OBJECT SUBJECT

ir.ACE .-SCREEN/Ftttf

( PHOSPHORS, ^JL DONOR TUBE SIDE

. I / * ^^..1 SCREEN

AgH FILM

DONOR NON-TUBE SIDE SCREEN

FIGURE 1. Typical Medical X-Ray Exposure Scenario (top), and Cross-section of Screen/Film combination cassette(bottom). 19 this scenario along with an enlarged cross section of the film cassette as 1t applies to the donor image generation. In 1 figure we find that this cassette actually consists of a silver halide photographic material sandwiched between two phosphor screens. It is the screens which make possible most medical imaging as we know 1t today. They do this by literally translating the energy of the Incident X-ray flux, via the phosphors, Into an energy band to which the photographic material is sensitive. Because of these phosphors, X-ray exposures many many times less that of direct X-ray imaging 1s possible. From a patient viewpoint then, it goes without saying that this 1s a desirable result.

Since no X-ray focusing is done between the object(subject) and image(screen/film) planes, the Image that one obtains upon development 1s in essence a negative shadow of the medium and its internal structure. Areas that absorb X-rays, Hke bone, Image with less density than flesh and muscle tissue which tend to let the X-ray flux pass. For instance, in Identifying a broken bone, the Image of the break will be dark against the relatively light surround of the bone. This 1s because the void created by the break allows the X-rays to pass, thus creating a higher density 1n the image. To a first order, this 1s the basic nature of the image used for medical diagnosis.

It is logical then to characterize the primary image of a medical environment by evaluating the Image generated by an X-ray screen/film system. Similarly, if any image enhancements are to be performed, it is on this screen film image that they would likely be done. With reference to the autoradiographic process then, 1t is natural in a medical imaging environment to define the donor as the screen/film image. Therefore, by definition, we have:

Donor- That image as generated by an X-ray exposure

onto a single screen/film system, and normal

chemical development. 20

"donor" From this point on then, the term will be consistent with the above definition. When necessary to distinguish only a portion of the donor system, that portion will be specifically stated; for example, donor film, or donor processing.

Recall that the receiver 1s necessarally born from the donor. That is, the steps leading to the receiver Image are not only those of the toning(or activating) and contact exposure steps but also of the entire donor sequence. In order to avoid confusion, the receiver as referred to earlier will from this point on be termed the "receiver-composite". It Is defined as:

Recei ver-composi te- That image as generated by the contact

exposure of the activated donor to the

receiver photographic material. This Includes

the normal chemical development of the

receiver material .

For clarification, figure 2 gives a block diagram of both the donor and receiver-composite systems. Having defined these, the necessary measurements to arrive at the DQE and NEQ of these steps should be reviewed.

From equation 15 we have

no9,n4)?tt(q))?lHTF(w))? D0E(..4) = q-W(w.q)

where q = Absolute log exposure 1n photons per unit

area

w = Rotatlonally symmetric spatial frequency

tf = Differential gamma(f1rst derivative) of the D-log q curve

MTF - Modulation Transfer Function

W = Wiener spectrum 21

*,*M***-1**" ' - " i rmitm r ~i

RECEIVER SCREEN FILM FILM

DEVELOP

DONOR If.AGE

l^DONOR IMAGE _ I

CONTACT ACTIVATE FXPQSURE

i RECEIVER COMPOSITE

TMflKF

RECEIVER-COMPOSITE IMAGE CHAIN

FIGURE 2. Block Diagram defining Donor(dash) and Receiver Composite(bold solid) stages. 22

In order to calculate the DQE and NEQ then, three primary measurements for both the donor and receiver-composite are necessary. Along with the type of samples required, these measurements are

1. Density vs. absolute log exposure(D-log q) or characteristic curves from stepped density patches to give $(q) and q.

2. Modulation Transfer Function from edge Images to give MTF(w).

3. Wiener Spectrum from uniformly exposed and processed density patches to give W(w,q).

Once the samples are obtained, their corresponding functions can be measured and calculated according to equation 15 to arrive at the DQE and NEQ metrics.

To insure an understanding of the image chain, figure 3

gives a block diagram of the steps involved In generating the donor

and receiver-composite samples. It also Indicates points along the

Image chain where the necessary parameters are measured or merged.

Keep in mind that all three sample types (i.e. step tablets, edges, and densiy patches) are being generated in this process. While the

details concerning the step tablet densities are discussed in this

section, those for the edge(MTF(w)) and density patches(W(w,q)) are

addressed in section 2.3. An entire listing of the major equipment

used in the data capture phase of this experiment 1s given in

Appendix A.

2.2 Saaple Generation

In performing the work described herein, every effort was

of a typical medical made to reflect the conditions imaging

environment. In this way, the work Involved with extending the

world should minimized. experimental results to the applied be 23

Conor Film (2.2.1) Receiver Film(2.2.1 I Sensitometry(t.?.2) Abs. Exp. (2.2.?)

Exposure(2.?.2) I

Develop(2.2.3)

Donor(2.2.3) Activate(2.2.3) Contact Exp. (2.2.4)

Develop(2.2.3)

Receiver Composite Donor Sample Sample

" Densitenetry(2.3.1)

D-log Q (2.3.2)

MTF (2.3.4)

Wiener Spectrum(2.3.6)

L DQE & NEQ T EVALUATE

Diagram for the FIGURE 3. Block

experimental procedure 24

2.2.1 Donor and Receiver Photographic Katerlals

The donor film was Kodak XG Medical Radiographic film.

This is a double sided green sensitive silver halide film with an emulsion thickness on either side of the film base of approximately

40 micrometers. The XG film was used in conjunction with a Kodak

X-Omat Regular screen. This is a barium strontium sulfate screen

"medium" and when used with the XG film 1s considered a speed

screen/film system.

The receiver film was Kodak NMC Nuclear Medicine film.

This was a single coated silver halide film and was chosen

primarily because of the promising results with It in work by

Vachon10 and Wheaton12.

2.2.2 Donor Screen/Fill Exposure and Sensltooetry

As indicated in figure 3 this portion of the experiment

is critical in determining the absolute exposure, q, necessary for the DQE and NEQ metrics. The exposing X-ray radiation was at a

nominal 70 Kvp(Kilovolts peak), 30 Mas(Mill1amp seconds), with .5 mm of copper and 1 mm of aluminum filtration. The spectral power

distribution for these conditions is shown in Appendix A, and was calibrated at 1.12 meters from the X-ray source. This corresponded

to 1.204 mill i roentgens with a 1% error from twelve replicate measurements made with an Ion chamber dosimeter. Exposure corrections for a temperature of 68F and barometric pressure of one atmosphere were made from this and then converted to units of 2 27 photons/cm via the standard photon fluence equation . An example of this calculation 1s given in Appendix B.

Once the absolute exposure at the above distance was determined, corresponding exposures at other distances were calculated using the inverse square law. The densities gave the usual stepped corresponding to these exposures density modulation used in obtaining the donor and receiver-composite 25

characteristic curves. It was felt that this inverse square law

sensitometry was most accurate since it avoided any scattering effects associated with stepped lead targets. The edge images were Created by contacting a copper edge on of the top screen/film sandwich and exposing at a number of distances from the source. This same trial -and-error technique was

also used for exposure of the uniform Wiener spectrum samples. Upon

development, those samples meeting the proper requirementsf to be

described) were then selected for measurement.

2.2.3 Chemical Processing

Two forms of chemical processing existed 1n this work. The one consisted of the usual latent Image to filamentary silver

development. This portion was carried out for both the donor and

receiver films in a Kodak X-Omatic film processor under the

manufacturer's suggested conditions.

The other chemical processing Involved the activating

solution of the subproportlonal bleach and S-35 nuclide. The choice

of this particular solution was made because of the success that

both Wheaton and Vachon had with this process. This particular

processing combined the bleaching and activating of the donor in

one toner step and eliminated many of the time consuming wash

Wheaton' stages. From s work, there appeared to be no adverse

effects with these shortcuts. The composition of the activating

solution along with the step by step toning procedures are given 1n Appendix A.

At this point, it becomes worthwhile to mention that

before the donor samples were activated, they were physically cut

1n half lengthwise. One portion was retained for the donor

characterization while the other was used for further processing 1n

receiver-composite. In this error characterizing the way. the caused by duplicate processing was minimized. 26

2.2.4 Receiver F11 Exjwsure

Once the activated donor was dried, 1t was placed emulsion-to-emulsion with the receiver film. This combination was then placed 1n a screen cassette and contact printed for 1.5 hours followed by the development process. This yielded the final receiver-composite.

Certain considerations were made 1n this step to allow for the double-sided nature of the donor film. Because the low energy beta particles of the S-35 nuclides are unable to penetrate the film base, only one of the donor emulsions was actually contributing to the receiver film exposure. The particular emulsion side chosen for contact to the receiver film was that side closest to the X-ray sourceftube side) at the initial exposure. This choice was made because of Its greater effective radiometric speed relative to the distant emulsion side( non-tube side). Since the tube side is closer to the X-ray source this result might be expected and is in fact confirmed in the results. Other reasons for knowing the tube and non-tube characteristics are made clear In the following Data Capture and Processing section.

2.3 Data Capture and Processing

From the previous section we have seen how the physical film samples to be measured were actually generated. Recall that these samples were stepped density tablets for the D-log q curve, edge Images for the MTF, and uniform density patches for the Wiener spectrum. It now comes time to examine the densitometric measurement of these samples.

Keep in mind that while all of the measurements are exposure space through the eventually refered back to D-log q original curve( see Introduction ), the basis for the measurements 27

He in the Initial densitometry metrics. With this In mind we will begin with the densitometry technique.

2.3.1 Densitometry- Macro A Micro

Macro-densities of the stepped tablets were read with a

Macbeth TD-504 densitometer in a visual diffuse mode equipped with a 3 mm diameter circular aperture. The edge Images and uniform density noise patches on the other hand were measured on a scanning microdensitometer. This was a modified Zeiss microscope/photometer with a photomultlplier detector and a computer Interface for rapid digitizationfsee Appendix A). For all microdensitometry, transmission values were the initial capture form. In order to lessen the effects of Inherent electrical noise 1n the microdensitometer, the recorded transmission values were an average of three replicate readings at each sampled point. These values were recorded over 0-225 counts corresponding to a 0-1 transmission range.

Whenever equivalent macro-diffuse density values were required, the micro transmission values, t , were converted to micro-density( i.e., -log(t )) which in turn were converted to macro diffuse density via a linear calibration curve. A different calibration curve was used for the donor and receiver-composite characterization and was arrived at through a simple linear regression of the macro (ordinate) vs. micro(abscissa) densities of no less than fourteen{14) different density patches over the range of expected density values.

Since the configuration of the microdensitometer for the

MTF and Wiener spectrum measurements were identical in many ways, the common parameters of the microdensitometer setup for the two are listed 1n Appendix A. The selection of these parameters was based on an average source wavelength of 550 nm, diffraction limited optics, 1.5 Index of refraction for the emulsion, and a

depth-of- 40.0 micrometer focus criteria. Microdensitometer 28

linearity and effective Incoherence conditions as described by 28 Swing were also observed for an Image scanning, overfill mode at a sampling interval of 12.5 micrometers. The calculations for the depth-of- focus, microdensitometer linearity, and effective Incoherence conditions are listed in Appendix B.

2.3.2 Characteristic Curve Data Acquisition

Data for all characteristic curves were read and reported

as macro-diffuse densities above base. From mlcrodensitometry

considerations that will become clear soon, seperate density

readings for the donor's tube and non-tube side were necessary.

This was done by stripping the emulsion from the appropriate side

of the film and measuring the remaining density on the substrate.

2.3.3 Characteristic Curve Data Processing

Remember from equation 15 that the DQE and NEQ analysis

required a differential gamma along each point of the D-log q

curve. To facilitate in determining this, all characteristic curves

were fit to a continuous function. The parametric equation for

this function was

D - D . max mi n * _J!i*. !"_ ?+ d.* D(x) uminD (16)

e-3(x-x) I +

where D Density

D = Maximum Density max

= D . Fog3 Density min */ = A parameter proportional to the maximum first

derivative of the D-log q curve

= Shift parameter 1n log exposure xo X = Independent variable in log exposure 29

Once the fit was satisfactory, the first derivative with respect to log q (1.e.,dD/dx 1n equation 16) was calculated in order to arrive at the differential gamma along any point of the characteristic curve. Qualitatively, this function worked quite well for the purposes at hand. RMS errors for the fits are listed in Appendix B along with examples of the raw and smoothed data.

2.3.4 MTF Data Acquisition

The edge images used for the MTF measurement existed over the non-zero slope portion of the characteristic curves and

subsequently digitized in transmission. Because of effective 29 exposure linearity considerations every effort was made to keep the density differences over the edge images to less than 0.30. The edges were imaged over three different mean density levels for the donor and two different mean density levels for the receiver-composite. Though these densities were all In the toe portion of their respective characteristic curves 1t was assumed

that the MTFs obtained from them were representative for all mean density levels. The validity of this assumption was not verified. For each edge image, fifteen replicate edge scansd'.e. same sample, different region) were read. Each scan consisted of 200 points and was measured with an effective slit dimension of 25 x 700 micrometers. All other microdensitometer conditions for the MTF data capture are summarized in Appendix A.

As mentioned previously, the double sided nature of the donor film deserved special consideration for both the MTF and

Wiener spectrum measurements. This was so because of the relatively large depth-of-focus needed to collect data from both the tube and non-tube sides of the donor emulsion simultaneously. This total thickness was 280 micrometers. Using an average wavelength of 550 nm and an emulsion refractive index of 1.5, one finds that a .036 numerical aperture(N.A.)efflux objective would have been necessary for concurrent-sided microdensitometry measurements (see 30

calculation in Appendix B). This efflux objective being unavailable, an alternative solution was sought. This solution 1s outlined below.

By stripping the emulsion from the appropriate side of the donor, the edge images corresponding to the tube and non-tube side of the donor were measured seperately. These seperate measurements allowed a relaxation of the depth-of-focus criteria to that of a single emulsion thlcknessd'.e, 40.0 micrometers). This criteria was therefore more easily satisfied(N.A.<.096) and was accomplished with an available .08 N.A. for the efflux optics. In actuality then, there were s1x(6) edge image samples measured for the donor, two for each of the three mean density levels. The way in which the seperate edge image scans were combined to arrive at the total donor MTF is covered in the following section. Since the receiver film was only a single sided film considerations of this sort were unnecessary.

2.3.5 MTF Data Processing

Having collected the edge scan transmission values, each individual scan was converted to macro-diffuse density and in turn effective exposure through the D-log q curve. All MTF processing was therefore done under the assumption that these systems were linear in effective exposure. While not within the scope of this research to confirm this, there was every reason to believe that at

prone the very least the donor system under consideration was not to the classical non-linear adjacency effects often associated with silver halide photographic materials. This 1s supported by the use

appreciable of non-viscous development and the unlikelihood of any laminar layer on the film when using the X-Omatic processor.

30 there was no Likewise, since all exposures were done at Mas, affected reason to believe that the sensitometry was by reciprocity

associated with silver halide affects, another non-linearity often photographic systems. 31

Because the fifteen replicate edge scans within a data set did not all begin at the same spatial coordinates, some effort was needed to place the fifteen scans in phase with each other.

This was necessary to avoid any positive bias errors in the

"1n-phase" averaging of individual MTF estimates. This operation was carried out visually as described below.

After plotting the points for the individual edge scans, the scans within each set were literally shifted along the distance axis and note made of the amount of shift for a satisfactory visual coincidence. The data files for each scan were then shifted 1n

software according to the previously noted shift values. The result was a single 3000 pointd'.e 200 points/scan times 15 scans/set) edge scan for each mean density level. The actual MTF calculation began upon completing this operation.

The method used for estimating the MTF was an edge 30 gradient Fourier transform scheme developed by Porth . Using this method, each 3000 point edge data set was fit with a constrained( zero-slope endpoint) least square cubic spline. Knot

positions for the spline were visually selected so as to minimize

the rms error yet retain the expectations of an edge profile.

Usually five, and no more than six knots were needed to fit a

particular edge data set satisfactorily. The Fortran callable

subroutine that calculated the spline, SPL2Z, and its intermediate values, SPLVAL, are listed in Appendix D along with other

calculation MTF supporting subroutines. Following the spline the transform of the spline's was estimated by calculating the Fourier first derivative. This was done via the subroutine SPLFTZ. An example of an edge fit with the splines is given in Appendix B. According to Porth30a typical 40:1 signal to noise ratio associated a l%-2% error 1n the with our edge data would give approximately

modulation. MTF at .50

Although differences between the MTFs for the tube and * expected no qualitative non-tube sides of the donor were

differences in the MTF estimates between sides were noted(see 32

Appendix C). microdensitometer* Therefore, after removing the s optical and aperture transfer function degradations, the six donor MTF estimates were averaged and taken as the MTF of the donor. The

same was done for the two receiver-composite estimates. In these cases the MTF averaging was rationalized because of the small

number of estimates combined.

2.3.6 Wiener Spectrum Data Acquisition

Digital transmission data for the Wiener spectrum was collected over ten different mean density levels ranging from .04

to 1.0 (above base) for a single side of the donor. The same number

of density levels was also measured for the receiver-composite film

and ranged from .14 to 2.68(above base). The specific density levels chosen were such that they corresponded to as near equal density increments as possible. The effective slit dimension for

scanning was 25 x 700 micrometers, and 52 data blocks of two-hundred points each were collected at each density level. This

(2/52)* 5 corresponds to a percent error 1n the Wiener spectrum at

(1/52)' 5 all intermediate frequencies and error at the zero and 32 Nyquist frequencies . Other microdensitometer parameters are as

outlined in Appendix A.

2.3.7 Wiener Spectru Data Processing

The Wiener spectrum for each mean density level was

estimated by direct digital computation of the equivalent macro-diffuse data from the uniform density patches. This involved

the block average technique which averages the Fourier transform modulus squared of a number of spectrum estimates at each

frequency. In this work, fifty-two(52) estimates per frequency (

f=.40 mm"1) were averaged. Further details of the block average 33 technique can be found in work by Dainty and Shaw . 33

Upon calculating the Wiener spectrum from the transmission values, the equivalent macro-diffuse density Wiener spectrum was in turn determined33. The error associated with this transformation never exceeded .4%34. A final correction on the spectrum was then made for the effects of the aperture and optical

MTFs of the microdensitometer. The Fortran computer program,

CLAUDE, that performed the initial Wiener spectrum estimation and subsequent corrections can be found in Appendix D.

Since the Wiener spectrum estimates were only for discrete density levels(ten per film type) and frequencies, some interpolation scheme to completely describe the donor and receiver-composite Wiener spectra over a continuum of densities and frequncies was necessary. This was accomplished by choosing an appropriate underlying function for the Wiener spectrum estimates

W(w). A descriptive parametric equation was then derived from this function from least square considerations and applied as the interpolation operator over all frequencies. This function used for both donor and receiver-composite Wiener spectra was

)2)q W(W) = h( 1 - ( + b (17) w max

A normalized (1.e.,h=l, b=0, and wmav=l) family of curves for this function Is Illustrated in Appendix B. The parameter wmax was chosen as 25 mm since Wiener spectrum values beyond this frequency appeared to remain unchanged .The parameters h and b are

for them were chosen essentially scaling factors and values by

plots of the low(w=.4 and visually Inspecting the log-log ) high(w= 25 mm"1) frequency Wiener spectrum values respectively at

order Interpolate across each mean density level. In to density and then a simple piecewise function was used to describe h b. This

spectra as a then characterized the rise and fall of the Wiener

Wiener and turn function of density. In this way, the spectra 1n 34

DQE and NEQ can be characterized over a density and frequency continuum. An example of a functional fit to equation 17 can be found in Appendix B.

Keep in mind that special care had to be taken for the double-sided donor film. This was handled by measuring and characterizing the Wiener spectrum for the single sided densities of the donor as described above. Once this was done, the equivalent double-sided Wiener spectrum was arrived at by simply adding the

Wiener spectrum values from the tube and non-tube side densities.

Choosing which two single sided densities to use was accomplished

through previous knowledge of the tube and non-tube characteristic curves.

The adding of the Wiener spectrum(variance) in this way 35 is well founded and assumes that the two image density patches

are Independent realizations. It also assumes that the final

detection system's depth-of-f1eld criteria covers the double-sided

film thickness. For normal viewing distances this 1s certainly the 36 case for the human visual system and becomes Important since 1t

is likely that NEQ could proportionally track with visual detection

performance. 35

3. RESULTS 36

With all of the measurements needed for the DQE and NEQ characterization of the donor and receiver-composite In hand, the exposition and outcome of these measurements are presented In this section. The individual results of the characteristic curves, gamma,

and MTF, Wiener spectrum are presented first. These results are then unified into NEQ and DQE parameters. Finally, none of the above would be complete without the proper error analysis. This 1s presented at

the chapters end.

Whenever possible, an attempt has been made to compare or verify the forthcoming results with that of previous work in the field. This is done primarily as a check to confirm that the metrics from this work reflect expected values and that no gross errors in the measurements were made.

Since the nature of this research cuts across the medical, physical, and engineering disciplines, the units, presentation, and nomenclature sometimes proved a problem in the preparation of this section. The decision was made to present the information in a manner consistent with the image science community. When appropriate however, supplementary graphs with a variety of formats are supplied in Appendix C. They are described and cited in the text whenever relevant. In an effort to promote uninterrupted reading of the text, all figures are presented at the end of the section.

3.1 Characteristic Curves - Gamma ff) and Absolute Exposure! q)

The resulting family of absolute characteristic curves for the different stages of the autoradiographic process are shown in figure 4. That is, the seperate tube and non-tube sides of the donor, the tube plus non-tube sides of the donor, and the receiver-composite.

these curves are gamma The necessary parameters derived from (dD/d( log

photon q)) and exposure(q). Since DQE and NEQ have their basis 1n

chosen in figure 4 are in terms of statistics, the exposure units 37

photons/cm . Supplemental graphs 1n Appendix C(figures CI 4 C2) are 2 plotted in exposure units of roentgens, and ergs/cm .

One possible point of confusion for the reader in these graphs may be the interpretation of exposure for the receiver-composite curves. One should not interpret this exposure as

the contact exposure from the beta particle flux. Rather, it should be

thought of as an effective exposure resulting from the enhancement of

the donor. In other words, the densities for the receiver-composite

were plotted at the same log exposure as those densities which created

them in the donor. With this behind us, let us proceed.

Below, table 1 gives a summary of the important points to be drawn from figure 4.

TABLE 1

Donor and Receiver-composite

Characteristic Curve Comparisons

Parameter Donor Rec.-Comp. Comment

.035 lower in 1) Fog density .048 receiver-composite

3.16 Approximate 2 stop 2) Speed .89 increase in rec.-comp.

Higher in Donor 3) 4.23 2.91 mavmax. Peak gamma higher in 4) Gamma 4.2 5.8 receiver-composite

Between opposite tube 5) Log Exp. shift -.08 sides

first four items, both Vachon's and With regard to the of the Wheaton's12 confirm the general nature work with this process for Item #2 are given In figure 5 and differences. Supporting graphs graphs function of exposure. Complementing Illustrate gamma as a log C4). as are given in Appendix C(figure Also, for gamma vs. density 38

Plewes37 suggested from discussions with the .08 log exposure shift of Item #5 accurately reflects the often used rule-of-thumb that for a given amount of incident energy the non-tube side receives 80% as much exposure as the tube side. For this experiment it was 83% as much. The reader is warned however, the exposure shift between tube and non-tube side as exhibited in figure 4 should not be Interpreted as an

absolutely greater screen/film speed for the tube side , but rather as

a means of segmenting the curves according to effective Incident exposure.

It was found that the shape of the donor characteristic

curve of figure 4 was in very good agreement with the results of work

(HHS)38 performed at the U.S. Department of Health and Human Services

for the same screen/film combination and development process (see

Appendix C, figure C18, for comparison). Likewise, the exposure needed to attain a density of 1.0 was comparable to values published by 39 Taylor under similar operating conditions( 75 Kvp, but with a moving bucky grid). His results were within 1 stop of those in this experiment.

3.2 Modulation Transfer Function - MTF(w)

Figure 6 shows the measured modulation transfer function for the donor and receiver-composite. Additional curves plotted on log-log axes are given In Appendix C(figure C3) and may prove beneficial in conjunction with the Wiener spectrum analysis. Both MTFs had the

- 1' x I general form of a negative exponential (i .e. , e l) with the donor MTF

cutoff at 8.0 and the receiver-composite cutoff at 4.0 . 40 Using Bracewell's definition of equivalent bandwidth as a mono-numeric for MTF comparisons, one finds that the donor's equivalent bandwidth is 1.8 compared to cfl.2 for the receiver-composite(shown in figure 6). This would Indicate that for the mid frequencies the MTF for the donor is 50% greater than for the receiver-composite. Checking this figure with the mid-frequencies

(.05-1.5 mm"1) generally confirms this. The guide used to check the 39

results of the donor MTF was from previosly mentioned work at the U.S.

Dept. of HHS . For the same screen/film combination, their MTF results compare favorably with the results of this work. A graphical comparison between the two is given in Appendix C( figure C20).

3.3 Wiener spectrum - W(w,q)

The final component needed before computing DQE and NEQ is

the Wiener spectrum. Representative curves for the donor and

receiver-composite Wiener spectra at a density of 1.0 above base are

given in figure 7. Included are the 95% confidence Intervals.

From figure 7 some observations can be made. They are,

1. The spectrum shapes are "well behaved". That 1s, both donor and

receiver-composite Wiener spectra exhibit the characteristically large low frequency values , gradually giving way to and riding

noise" on a lesser, but constant, "white component . This shape

is common for screen/film radiographic imaging systems.

"whitens" 2. The Wiener spectrum for the donor and

receiver-composite spectra atss25. .

3. The spectrum shapes are different from one another in that the

Inflection point of the donor's spectrum( 1n log-log coordinates)

occurs at fairly low frequencies while that for the

receiver-composite appears at the higher frequencies.

4. For low spatial frequencies and equal densities, the Wiener

spectrum of the receiver-composite is approximately an order of

magnitude greater than for the donor.

In addition to this, the absolute values of the Wiener spectrum forthe donor conforms well to the measurements of reference 38. These are illustrated in Appendix C(figure C19).

Although figure 7 and the above results are instructive, one

order characterize the DQE 4 must keep in mind that in to NEQ must be done with respect to two according to equation 15, it 40

independent variables, spatial frequency(w) and exposure(q). Since the Wiener spectrum is a function of these variables, It should be analyzed from this perspective. An attempt in depicting the three dimensional (x,y, 4 z) Wiener spectra is illustrated via contour plots 1n figures 8 and 9. The x axis is spatial frequency; y axis log exposure; and z

axis(coming out of the page) Wiener spectrum. Shown are contours of

equal log Wiener spectrum values in absolute units of D2um2, and most

are labeled to avoid any confusion. Each successive contour signifies

an equal log Wiener spectrum difference from its nearest neighbor, and corresponds to an approximate 26% change from it. Appendix C gives

additional plots with density and spatial frequency as the independent

behaved" variables. These are presented to convey the "well nature of the spectra with respect to both spatial frequency and exposure. By taking a log exposure cross-section of figures 8 and 9,

at particular frequencies a clear picture of the Wiener spectra values behavior at these frequencies as a function of exposure is evident.

Choosing as the Wiener spectrum frequency of peak value, and 2.0 as a compromise frequency for the half peak Wiener spectrum value of donor and receiver-composite, figure 10 illustrates that the

shape of the Wiener spectrum vs. log exposure relationship for the donor and receiver-composite is largely insensitive to spatial

frequency- Therefore, in order to simplify the analysis, most of the discussion from here on will imply a low frequency (i.e. ,.40 ) definition of the Wiener spectrum and in turn, DQE and NEQ. Any necessary extensions to the higher frequencies can be had through figures 7,8, or 9, or the contour plots in Appendix C. Using the above approach in figure 11, one can observe the trend of the low frequency Wiener spectrum as a function of log exposure. Included in figure 11 are accompanying plots of the donor and receiver-composite characteristic curves to help with interpretation in density space. From this, one finds that the Wiener

exposure level. That at least spectrume is fairly linear with log is, than 1.2 in the case of those exposures leading to densities of less 41

for both donor and receiver-composite. Beyond this density, a sharp Wiener spectrum falloff of the receiver-composite occurs along with a more gradual flattening of the donor Wiener spectrum at*J2.0 density.

3.4 DQE and NEQ

Finally, the DQE and NEQ of the donor and receiver-composite are calculated by unifying all of the previous results according to equation 15. The results for the donor are illustrated in figure 12

for a frequency of .40 mm"1. The characteristic curve in relative density is also given for comparison purposes. Additional contour plots for the entire bandwidth are given 1n Appendix C(f1gures C9-C16) and support the previous contention of shape insensitivity with

spatial frequency.

Both the DQE and NEQ of figure 12 compare well with the few SNR values that exist for X-ray screen/film systems. Work by Wagner 43 and Muntz predict maximum DQEs on the order of 30% while Wagner

44 _ -2 alone lists NEQ values at typical operating points of ".05 um . For the donor screen/film system tested the values just cited both occur at a density above base of 0.63. DQE and NEQ results for the receiver-composite are given 1n figure 13 with the appropriate contour plots in Appendix C. The shape of the DQE and NEQ curves for both the donor and receiver-composite along with the location of their maxima along the characteristic curve are consistent with most silver halide film systems. DQEs will typically reach a maximum in the toe of the characteristic curve, while maximum NEQ occurs at maximum gamma. Physically, this is due to the thresholding and saturation nature of the silver halide

"receptors". A summary of the important points from figures 12 and 13 are listed in table 2. 42

TABLE 2

.1 Maximum DQE 4 NEQ G .4

Donor Receiver-comp (F1g. 12) (F1g. 13)

DQEy 0.30 0.21 max Log Exp. (photons/cm ) 7.26 6.78 Density (above base) 0.63 0.75

(um"2) 0.08 0.018 NEQmAmax p Log Exp. (photons/cm ) 7.55 7.03 Density (above base) 1.80 1.90

With these results presented, an estimate of the error

involved with their calculation is now 1n order. Therefore, as a

fitting ending to this section, that which follows will detail the proper error analysis of DQE and NEQ from their component

measurements.

3.5 DQE and NEQ Error Analysis

Throughout the experimental section, figures for percent

error(

possible. These estimates are listed in Table 3 below, along with some

reasonable guesses for the gamma error. Before proceeding however,

some background is necessary.

One can determine the total percent error 1n DQE due to the components in table 3 through equation 18 below. It 1s * r- -,2 nZ ^Z _ ^r r, 07 s. 4-' (18) DQE 43

In each case, signifies

By actually substituting the component percent errors of table 3 into equation 18, the right most column of the table was

generated .It should give the reader an idea of the way that the component errors are propagated.

TABLE 3

Percent Error Values in Calculating DQE and NEQ TlATf/ TbgE, ^ / ?t / * / WS / MIT/ DQE,

10. 20. 28.

10. 13. 24.

20. 22.

5. 13. 17.

0. 2. 20. 20.

.4 13. 14.

One finds that while most of the individual errors are within reason, the fact that they are either multiplied or even worse, squared, leads to some unacceptable errors in DQE. In fact, by performing an actual calculation one will find that the largest contributors to the DQE error are the individual gamma and MTF( the only difference between

DQE and NEQ is the exposure term in the denominator. Therefore, since the exposure error is relatively small in this case the same 44

conclusions for the error in DQE can also be made for NEQ). Indeed, 46 this is why many researchers are reluctant to measure It .

With this in mind then, certain doubts may be cast upon the precision of this experiment. This author makes no claim to the contrary. Let it be known though that as a result of the assumptions

in the above analysis, those figures cited, are to be interpreted as a

root-mean-square error and not as one of miscalibration or bias. It is

"accuracy" clearly a difference between the definitions of and

average" "precision". Therefore, "on the the results of this experiment

must be are certainly accurate, and as with any measurement the user

aware of how far to extend the results to his particular application.

Further discussion of these results follows. 45

B.OO,.

F1

4.00

Donor

a. oo..

e.oo. Receiver it Composite 5 I 1.00

0.00

Ads. Log Exposure { photons / so. cm. J

Figure 4: Characteristic curves for

different stages of the

Autoradiographic system tested 46

6.00.,

Receiver Composite

3.00.. $

2.00..

1.00..

cd to f^ r-. r- r- CD oo

A/7S. Log Exposure /'p/totons / so. eg. J

Figure 5: Differential gamma vs. log exposure for Donor and Receiver Composite 47

1.00

0.90. \\ 0.80. 1 \\ 1 0.70. \\ T DONOR 0.60. \ft \ \ O.K. \ \ I \ 0.40. \1 \ \1 0.30. \ \ \ 0.20. \\ RECEIVER COMPOSITE

0.10. \ V,

*<"" 0.00 1 1 4 1 1 1 4-=a H II I T *^ 1 I II I 8SSSSSS8SSS ...... o-4rum^iocD-4.o

Spatial Frequency fcycles /m. J

Figure 6: Modulation Transfer Functions for Donor(dash) and Receiver Composite(sol id) stages 48

100. V

onfidence

nterval

10. ;

D

i i i i i ui I I I |nr| "I i i i i 1 1 1 o

o o o

Spatial Frequency ( mm-1 )

for Donor Figure 7: Wiener spectrum(W(w)) and Receiver Composite at 1.0 Density above base 49

vi

\ 1 I i

I

8 8 8 8 8 988S888 8888881 8 8 8

SpatJaJ Frequency f cycJes /J

Figure 8: Wiener spectrum contour plots for Donor. Equal log noise power intervals 50

S I t I 4?

l

8 8 8 g 8 8 8

SpatJaJ Frequency / cycJes /mj

Figure 9: Wiener spectrum contour plots for Receiver Composite.. Equal log noise power intervals 51

Receiver Composite

100."

' mm-1 .40 2.0 mm-1

^eIO.

CM O

1 "

t r - vn ?D 1 1 1 T ID

vo f~4

Absolute Log Exposure(photons/cm2)

Figure 10: Wiener spectra values t? .40 mm

(solid) & 2.0 mm (dash) for

Donor & Receiver-composite 52

100."

10.-

CM O

Absolute Log Exposure(photons/cm2)

Figure 11. W(.40) for Donor(solid) and Receiver Composite(dash) compared to respective characteristic curves Wiener spectrum on left ordinate & density on right ordinate 53

C\J

E

03 fe

o Q

Absolute Log Exposure(photons/cm )

Figure 12: Donor DQE(solld) and NEQ(single dash) mm-1. curves

characteristic curve for comparison. 54

/ *NNEQ

CM N . / .- I o '

i* / *

cS.20:

S- QJ > O .4 c_> QJ o s- CD cu ^^ 1-H V CC > -// 1 / \ o * QJ J ,!!] / \ CC ^-B--Z5 \ s *

O LO LO

r-. VO 44

Absolute Log Exposure (photons/cm2)

& Fiqure 13: Receiver Composite DQE(solid) NEQ(single dash) curves @ .40 mm"1. curve Relative Density characteristic for comparison 55

4. DISCUSSION 56

With the results of the measurements having just been presented, questions "how?" "why?" relating to the and of these results need to be answered. It is the purpose of this discussion section to answer these questions or, at the very least, speculate on them. If appropriate, recommendations for further research will also be made.

Although DQE and NEQ are the primary metrics of interest in this study, 1t would be wise to investigate the fundamental quantities that influence them. In this way, any efforts to Improve system performance can be directed toward those components offering the

*6* greatest gains. These components are speed(l/q), gamma ( ), MTF, and

Wiener spectrum. Recall that they are mathematically related to DQE through equation 15 which is restated below.

no910e)2Wq))2(MTF(w))2 DQE(w.q) - (lg) qW(w,q)

Simply put, equation 15 tells us that the speed, and the squares of

MTF and gamma lead to proportional changes 1n DQE, while the Wiener spectrum yields reciprocal changes. Of course, with the exception of the speed criteria the same holds for NEQ.

The chronology in this section is similar to the others. By beginning with an analysis of the characteristic curve, the influences of speed and gamma on DQE are studied. This 1s followed by a discussion of the influences of the final two components, MTF and

Wiener spectrum. All four components are then unified under the DQE and NEQ section along with some appropriate applications.

4.1 Characteristic Curves

donor to The gains in speed and gamma in going from receiver-composite were expected, and as cited 1n the Introduction, the S-35 are consistent with past results9"12. This 1s because

silver grains in the nuclides are able to amplify the individual 57

extreme toe of the donor curve that are usually undetected by typical optical densitometric techniques. This amplification has led to a resultant speed in the receiver-composite that Is consistent with "fast" X-ray screen/film systems38'46. Earlier, it was stated that the donor screen/film system "medium" was considered speed. By analogy we "medium" "fast" then, have effectively gone from a to a screen/film

system.

Relative to previous S-35 processes, the speed and gamma increases are due to a considerable .eduction in the

receiver-composite fog level. A receiver-composite with lower fog

decreases the Wiener spectrum values in the toe of the characteristic curve, and in so doing enhances the DQE and NEQ. This was shown by Shaw in a model that revealed that fog acts not only as a seperate

noise source, as one might expect, but also in a multiplicative way on

the input photon noise. This multiplicative effect is a result of the

fog grains reducing the film gamma in the toe of the characteristic curve. From equation 15 then, it is plain to see that DQE along with

NEQ are affected multiplicatively by the square of the gamma. Hence, any significant change in this parameter is likely to have a profound effect on the DQE and NEQ.

Based on these facts alone, it might appear that the DQE and NEQ of the receiver-composite are prone to exceed those of the donor. This is suggested by the large gamma differences between the two stages. These differences are made clear in figure 14 and show that there is a maximum lOx difference between the receiver-composite and donor gammas for any particular exposure. Though this opportunity for large signal enhancement might appear appealling at first, there are tradeoffs that go with 1t.

One of these tradeoffs 1s shortened exposure latitude. Indeed, from figure 4, this is exactly what has happened for the film receiver-composite, and it 1s made worse by the fact that the NMC used for the receiver-composite has a lower than the donor's XG Dmavinaa film. Therefore, while one might expect a shift in the DQE and NEQ

latitude" lower "exposure (not strictly defined for DQE and NEQ) to 58

10.0 -

Receiver-Composite gamma: Figure 14: Ratio of

Donor gamma vs. log exposure 59

exposures due to the speed increase, an extension of this latitude to these exposures does not occur. This Is due to the low D of the max. receiver-composite film which by necessity leads to a premature falloff of its gamma 1n the exposure region where the donor's gamma is

still maintained. (Figures 12 and 13 should help in visualizing this.) other The tradeoff of the receiver-composite's increased gamma is

corresponding noise enhancement. This, of course, 1s covered through

the Wiener spectrum characterization of the receiver-composite. Before

analyzing it though, we will consider the MTF and its influence on DQE

and NEQ.

4.2 Modulation Transfer Function (MTF)

Considering the many opportunities for scatter and

refraction afforded 1n an X-ray screen/film system, the MTFs of figure

6 are not surprising. They are consistent with not only the physical aspects of the imaging system (grain size, # of Interfaces, 38 thickness), but also with parameters from previous experiments on

medium speed screen/film systems. Specifically, these parameters are

equivalent bandwidth, shape, and cutoff frequency.

"medium" Just as the donor's MTF parallels a speed

screen/film system, the MTF of the receiver-composite is similar to a

"fast" 38 typical screen/film system . Figure 15 Illustrates these

comparisons for both donor and receiver-composite analogies. For the

receiver-composite, it shows that while the low frequency modulation

"fast" of the receiver-composite is similar to a screen/film system,

the cutoff frequency for most of these systems extend beyond that of

the receiver-composite. If, however, one is willing to overlook this

stated for the same lack of equivalence, it can generally be that,

tradeoffs 1n speed and MTF, going from donor to receiver-composite is

"medium" "fast" screen/film system. comparable to going from a to a

Since much of the DQE and NEQ analysis Is done at ,

receiver-composite at this the difference in MTF from donor to

= MTF(.40) .95, and for the frequency should be noted. For the donor, 60

oo CO to 00 E CO CU

to >) to CO E r- O Ll_ a. r 4^^ E u_ C O 4 cu v_> c cu LL. 1 cu s_ cu c h- S- QJ u +j cu s: cu i- CO r- CU > o to S- i- r LO D o u o CU CU Q- to c u -o CU E o CU cu Q. O T3 o CC cu to (_> Ol Q. I OJ -o T3 to r J- O. cu CU E CU to s- S- r 3 > 3 3 4-> "4 tO to to -o CU ro m (C OJ u CU cu Li. s cu T5 s: s: = = cc CU CO -o c n3 -o c s- (0 o c o to o

O i ro c o o 1/1 Q.

r- s_ IO a. E +J o c_> 5

a>

3 cn

U0L-tBLnPW 61

= receiver-composite, MTF(.4) .90. These figures will also affect the

DQE and NEQ by the square of their respective values. One should be

reluctant however to translate these into any meaningful measure of radiographic image quality. This is so because of the combined effects 48 from several sources , the most prominent of which Is photographic

noise. An analysis of this noise for the processes at hand follow.

4.3 Wiener Spectrua

A distinguishing feature of medical radiographs is the

somewhat splotchy nature of the image structure. This characteristic

noise or mottle has appropriately come to be known as 'quantum mottle'

since it arises mainly from the statistical nature of the X-ray

quanta. When analyzed via the Wiener spectrum, one finds that this

mottle manifests itself as a dominant low frequency component that

gradually gives way to, and rides upon additive noise contributions

from screen structure and inherent film grain. For most screen/film

systems the mottle component completely falls off at Si 25 . From this frequency to about 50 mm. the sole contribution to the Wiener

spectrum is from the screen and film grain sources. Beyond this, the

Wiener spectrum is typically nil. These characteristics of X-ray

systems' screen/film Wiener spectra have been modeled by Rossman and 49 further studied through exposure radiation experiments by Halmshaw

Rossman' A diagram of s model along with Its functional form 1s given

in figure 16.

Since the Wiener spectra of both the donor and

receiver-composite assume the general shape of Rossman 's model , it

that point of view. For would be interesting to analyze them from donor and receiver-composite Instance, as far as the shape of the quiet well to Wiener spectra are concerned, both appear to conform

quantum mottle that of Rossman's model: low frequency gradually giving

screen structure and grain noise. Since the way to higher frequency X-ray/screen interaction mottle is a direct consequence of the though,

this same effect appears in the one may question why 62

toEECT.lifiRAlN^ \

K^|A(w)l2 = iGRAIN +

y&

w ( w\~h

ROSSMAN'S MODEL FOR X-RAY SCREEN/FILM SYSTEM

WIENER SPECTRA

| = Wiener Spectrum or Noise Power

G = System Gain

nx = Avg. Absorbed Quanta/Area A(w) = System Transfer Function

Figure 16: Schematic of Rossman's Wiener

spectrum model for radiographic

film/screen systems 63

receiver-composite spectrum when in fact no screen Is used to expose the receiver-composite film itself. It is speculated that the low frequency mottle of the receiver-composite 1s simply a manifestation of that in the donor.

through" That is, some sort of grain "print effect Is probably occurring in the contact exposure between the donor and receiver-composite films. Whether or not this print through of the autoradiographic process 1s governed by the same theories put forward for classical two-stage printing processes 1s certainly an area for further studies.

By further extending Rossman's model to our results however, a quantitative discrepancy occurs. That is, the experimental results of this research do not support the low frequency fall off of the Wiener spectra with the square of the MTF as predicted by Rossman's model.

For both donor and receiver-composite, the Wiener spectra clearly fall off slower than this (see figure 17), thus Indicating sources of noise 43 that are not influenced by the MTF . This anamolous behavior is more pronounced for the receiver-composite and qualitatively might be expected from the complex nature of the process up to that point. Having analyzed the Wiener spectrum as a function of frequency via Rossman's model, it now becomes appropriate to discuss this same Wiener spectrum values as a function of density. Doing so,

occurs. yet another departure of the Wiener spectra from a past model linear This model is Selwyn's Law42. While Selwyn's Law predicts a relation between Wiener spectrum values and mean density level, this illustrated in figure 18 for the donor study shows otherwise, and is with the . familiar and receiver-composite at .40 For those

should come as no pragmatic end of photographic science, this Law grain surprise. Because assumptions in Selwyn's governing

almost all silver halide statistics are violated at higher densities, behavior. The donor and photographic materials exhibit this

exception. An analysis in this receiver-composite densities are no departure from semblance of regard shows that for the donor the any

of * and appears to approach an linearity occurs at a density 60, 64

r 0*01

cu c cu --.-i-.

CD

r s_

cu

..

to o o. E o CJ

S- . VII VNJ > u_

r- 1 cu s: O CU CU cc > ^ -a 4-> a-awcy BAiiviay c o ro cu D. ^"4 to +-> 01 ll- s- CU 1 s_ ^^ r- O'OI s- CU o .c c +j o o -i-> to <4- c o r- ro c CD o ro to ^ ro i- S- (C +-> Q. o 6 E CU o Q- CJ to

cu s. 3 CD

a3MDd 3MlVT3y 65

IOOC.Ot

J?ECEI\R-aw>05I7E

100.0- -

o

DONOR

10.0--

8 9 S S S 9 8 8 8 R s s 1 i-H l t r 1 i 1 CNJ CM CM CM TOO-DIFFUSE DENSITYCabove base)

Wiener spectrum Figure 18 : Low frequency( .40 mm"1) Receiver-Composite value for Donor and

vs. Macro-diffuse density 66

2 2 asymptote at 25 D um . For the receiver-composite, the Wiener spectrum is characterized a by nearly symmetrical rise and fall about a density of 1.30. Based on new models of image structure36, this falloff of the Wiener spectrum at higher densities Is likely attributable to grain clumping.

Up to this point, we have analyzed the donor and

receiver-composite Wiener spectra in and of themselves. If however,

there is a greater interest in SNR gains from donor to

receiver-composite a comparison of the spectra 1s 1n order. This

comparison should indicate whether gains in signal power (gamma or

MTF) are offset by equal or greater gains in the Wiener spectrum. This, of course, would suggest a net loss in SNR transferring from donor to receiver-composite and thus lower the DQE and NEQ in the

receiver-composite.

The increase of the receiver-composite gamma might be

chiefly responsible for such an effect. This Is supported in both

Rossman's model and classical noise transfer theory which requires the Wiener spectrum of a printed density be proportional to the gamma squared of the printing process's characteristic curve. Therefore in

attempting to predict whether the receiver-composite's Wiener spectrum

might outweigh any signal increase, the square of the

receiver-composite's gamma would be a useful predictor. Since it 1s

presumed that the donor gamma at a given exposure leads to a

receiver-composite gamma at the same exposure, it 1s only proper that

comparisons of the Wiener spectrum be done on an equi-exposure basis.

This being the case, one finds that the receiver-composite's maximum

gamma of 6 (figure 5) would only account for a portion of the large

measured increase in equi-exposure Wiener spectrum. Interpreting this in terms of DQE and NEQ 1t Is found that the numerator although a 36(i.e.,62) fold signal increase results In

than offset the average 2 order of of equation 15, this is more by

receiver-composite 11). magnitude noise Increase from donor to (figure greater than of The fact that the Wiener spectrum does increase by %

classical noise transfer the receiver-composite may tell us that 67

theory is not applicable to the autoradiographic process. This was alluded to earlier when it was pointed out that unlike typical two-stage expose-to-print processes, the silver 1n the first stage(donor) no longer acts to attentuate radiation but rather to create 1t. Herein may lie the reasoning to the large noise Increases

1n the receiver-composite, and is certainly an area for further

research in understanding noise transfer for the autoradiographic

process.

From this information then, increases in DQE and NEQ for

the receiver-composite step would not be anticipated. We find that this is Indeed the case despite the folding in of MTF & exposure influences. A detailed discussion including the implications,

interpretation, and significance of this follows.

4.4 DQE and NEQ

In the introduction, it was pointed at that three questions These along with the hypothesis were to be answered and addressed.

questions were

donor or 1. Is the DQEmax or NEQmax greater 1n the

receiver-composite?

2. How do the DQE and NEQ between donor and receiver-composite

compare on an equi-exposure basis?

expose-to-print is the 3. When treated as a two stage process, in the donor the same as that for exposure at DQE av step

NEQ in the receiver-composite step? max

these questions in mind in this The reader Is reminded to keep

of them deal with DQE and particular section since, all ultimately

answer these questions in the NEQ. It is the author's intention to

forthcoming discussion.

the of .21 exhibited a For the receiver-composite, DQEmax on these from the donor's of .30. Based substantial decrease DQEmax 68

peak values one then, could conclude that when treated as seperate the imaging systems, receiver-composite offers no advantage over the donor in efficiently detecting incident quanta. Indeed, at their maximum DQE the values, receiver-composite was only 66% as efficient as the donor. A much greater decrease was evidenced with respect to the values. The NEQ difference in the maximum NEQ of nearly 350, %

clearly indicates the superiority of the donor in a SNR sense. The answer to the first of the above questions then is, the donor exhibits

greater maximum DQE and NEQ than the receiver-composite.

The overall lower DQEs and NEQs exhibited by the

receiver-composite were no doubt due to the greatly boosted Wiener

spectrum values in the intensification step . From this, 1t would

appear that, the worse fear concerning the intensification step's

enhanced gamma increasing not only the signal but also the noise was realized. That is, along with signal amplification came

disproportionate noise amplification. This was especially evident for

the NEQ parameter since the increased speed of the receiver-composite

did not figure in its calculation. This additional speed contribution

of the receiver-composite did help to bring the DQE,V for this step

to within a reasonable limit of that of the donor, and is encouraging

when one analyzes the donor and receiver-composite on an equi-exposure

basis.

Recall that the appropriate analysis for certain cases may

not be one of comparing maximum DQE and NEQ as much as comparing these

parameters for a given exposure. In this way a normalizing of the

quanta noise is achieved and comparisons can be commensurate over all

exposures. The extent and nature of the DQE and NEQ transfer should

likewise be realized from this. These comparisons are illustrated in

figure 19. Here the ratio of receiver-composite: donor DQE levels are

exceed for plotted against log exposure. Should this ratio un1ty(l) intensification process would be worthwhile to any given exposure, the plain see figure 18 exploit at these exposures. Though it is to from

was that this is not the case, the fact that a ratio of unity closely

106*75 photons/cm2does offer promise. approached at an exposure of 69

1.00.

O.N.

o.eo.

4, 0.70.. 5

0.50..

C^1 0.40.

ix 0.30.

(^ 0.20.

0.10..

,_ 1- | I 1 1 1 t 1 I I 1 1 II < 1 ' 0.00 J -I I 1 1 1 -| 1 1 1 CM cs 44! m

Ads. Log Exposure f photons / sq. cm. J

Receiver-Composite:Donor Figure 19: Ratio of DQE ( & NEQ ) ratio vs. log exposure 70

With further research 1t should not be difficult to find a different material or processing that would reduce the effect of the Wiener

spectrum, while keeping other parameters constant & in turn Increase the receiver-composite's DQE. In so doing, the receiver-composite: donor DQE ratio is likely to exceed unity and thus present an opportunity for more efficient quanta detection over that

of the donor. Whatever the scheme, it is not difficult to see that a

minimal increase of the receiver-composite DQE would accomplish this.

As a matter of fact, the same holds for the NEQ of the process also. The reasons why follow. While NEQ comparisons are typically done on an equi -density

basis , this form of evaluation makes an implicit assumption that one

is interested in, for example, the receiver-composite as a detecting

entity by itself. That is, as opposed to an enhancer of an existing

process. One would change exposure in the print step to suit some

output dynamic range in the former, whereas this is not true for the

process at hand. In the context for which visual detection increases

were noted by previous workers, the latter is more accurate. With this

as a basis, we can answer the second of our questions on both

equi-exposure DOE 4 NEQ through figure 19 alone. The fact that DQE 1s

no more than an exposure normalized NEQ allows us to do this.

Therefore, from a SNR viewpoint it appears that the receiver-composite

offers no advantage over the donor. 9-12 How then can we reconcile the unanimous reports of

increases in visual detection in the receiver-composite when 1n fact

the NEQ do not reflect these increases? Certainly one way to coordinate the two is to recognize that figure 19 gives no information

zero. below an exposure for which the donor's gamma is effectively

Since the donor's gamma 1s zero (see figure 5) then by definition (equation 15) the NEQ 4 in turn the SNR of the donor for exposures for the less than this are also zero. This is not the case however. One can see receiver-composite at these same exposure levels, from figure 5 that the receiver-composite's gamma remains essentially

more than for the donor. This is non-zero for at least one full stop 71

the key in that recognizing 1n this exposure region .the receiver-composite will necessarily have a higher SNR than the donor and in turn, contribute toward increased signal detection. in Unfortunetely, this experiment, sufficient data for confident characterization of the NEQ in this exposure region was not collected and is indeed a shortcoming of this work. Consequently, making any decision concerning the original hypothesis about the NEQ 4 DQE in

this exposure region would not be wise and is best left for verification by future workers.

The above rationale, though certainly plausible, would seem

to account for only a fraction of the reported increases in

radiographic interpretability; especially when one considers that historically only a small portion of the signal occurs over the area of the characteristic curve just cited. Something more fundamental Aft must be happening. In this author's estimation, 4 apparently others

"something" this is the human visual process.

Unlike unintelligent, memoryless detectors, the human visual process bases its detection 4 decision making on a complex psychology of pattern recognition tasks. This is the perceptual process of the 48 radiological process eye 4 brain. As pointed out by Goodenough , the can be thought of as a series of five operations. In order, they are exposing, recording, display, detection, 4 recognition. This paper has quantified the first three 4 perhaps a portion of the fourth. With an entire host of parameters ranging from the number of signals detected to observer a priori knowledge to consider, 1t should not be difficult then to understand the mismatch between this studies results

4 increased visual detection by experienced observers. This is supported by Goodenough in his study of image quality on medical diagnostic decision making. In this he concludes:

"...there are many unknown factors Involved in the pattern

tend to obviate a general recognition step of diagnosis that known predictive equation of diagnostic accuracy from

parameters." physical 72

It 1s speculated that somehow, someway, the human visual process is able to selectively mask the noise from the signal and, in "through" so doing, see the increased noise of the receiver-composite without suppressing the signal. Another thought 1s that, quite simply, the intensification process Increases the SNR for the receiver-composite above a certain visual threshold which did not

donor' exist in the donor, namely in the toe of the characteristic curve. This reasoning reflects the insufficient data collection cited

evidence48 previously. Finally, there is even to suggest that some traits which contributed to low NEQ, namely high granularity due to high gamma, may have actually increased human detection performance.

None of the above should be taken as a denunciation of SNR as a detection criteria however. It is simply that SNR does not tell the entire story, especially in cases involving the human visual process. Furthermore, it does not imply that the results of this study cannot be used to optimize what is still the common denominator of all detection criteria, that of SNR. Some ways of doing this are outlined in the following applications section.

4.5 Applications of DQE and NEQ

In the previous section, two of the three questions

answered. two were originally asked in the Introduction were The first concerned with comparisons between donor and receiver-composite for 1) maximum DQE and NEQ, and 2) equi-exposure DQE and NEQ. The third

"handshake" question on the optimal between donor and receiver-composite was left begging however. This was done because it

section. was more appropriately answered in this

Recall that the foundation for the third question lies in

expose-to-print SNR optimization considerations for two-stage

donor and receiver-composite as processes. Rather than treating the

question "Is there some seperable imaging systems, the becomes, way when considered as a two-stage that their interaction can be optimized For where exposure criteria is critical printing process?". example, 73

(in the recording stage or donor) one would want to base exposure on maximum DQE. On the other hand, 1f there was no limit to the amount of available energy (the printing stage or receiver-composite) the exposure should be based on maximum NEQ. Therefore, in extending this logic to the autoradiographic process, one would want the exposure at maximum DQE of the donor to coincide with the exposure for maximum NEQ

1n the receiver-composite. In this way the maximum output of the receiver-composite is statistically matched to the most efficient output of the donor.

By turning to figure 20, we find that the statistical match between donor and receiver-composite is not optimum. The peak DQE of the donor is approximately 1 stop removed from the peak NEQ of the receiver-composite. If however, one was asked to make a best choice

"handshake" 7 ' 12 for the optimum exposure, an exposure of 10 p photons/cm would appear a reasonable compromise since the values for donor DQE and receiver-composite NEQ are both within 90% of their maximum at this exposure.

A parallel scheme to the above that has also been suggested is the composition of several images exposed at DQEmax to give a SNR greater than a single image exposed at NEQmax. While this composite of images could be achieved a number of ways , the most obvious, but also cumbersome, method would be to physically register

"n" the images together. This is, in fact, exactly what occurs in motion picture viewing and is the reason why the image quality appears

"moving" much better for the image than it does for a single frame.

The basis for this lies 1n equation 19 which relates the composite SNR

"n" exposure which of registered images 1n terms of the NEQ at the for

DQE is a maximum. It is

(19)

given Appendix B. The integer The derivation for equation 19 is in "n" "n" chosen so that times the value of for a given application 1s

greater than the exposure at NEQmax. An exposure at DQEmax will be no 74

( Z-wn j o3N jaAraoatf cu o o o o I- 08 L cu

to o OLL CL E 8 O C_) 087 S- cu c > o OBZ cu +J \ (J ro cu 3 CC OfI ro > cu

Of I CD c

i- c OZL o 5- to CL

cu cu OTV o- CD o ro

to -> o s- to CL 007 o i E c o o o 5 C_) o +J OBB s- - s- CU o o > K- (Z cu 088 o ^-~. o to x: cu ^ to s- ro T 01 B ro X3 CL 4< I E o- O UJ c_> Z OBB

o CM * ' ?* -t 1 l l 1 I l 1 OS"B cu o o o s- 0) ru o 3 CD

300 Jouoo 75

for analogy this is, for a given amount of energy can the job be done better through many small hits of the hammer, or with one big hit. In other can words, better SNR be achieved with many lesser exposures or one single one. To answer this question, an example 1s In order.

"n" Take for instance the donor. In this case turns out to be

Exposure P NEQ,max n = 10 (7.55-7.26)= 2

Exposure 0 DQE max

In order to determine the percent gain in SNR for the composite image,

one simply normalizes by the bellwetherbellwethf of SNR, or NEQmav. Therefore, by normalizing equation 19 one obtains

( n- NEQ( 0 DQE) max SNR gain (20)

NEQmax

Substituting the appropriate donor values into equation 20 then

2- (.05)

SNR__,._ _ gain - 1.11

.081

In other words, by using a 2 image composite, each Image exposed at

achieved as for the same exposure as DOE . an 11* gain in SNR is DQEmax

NEQ'max Translating equation 20 for the autoradiographic process at hand, the maximum SNR gain can be written as

.5 (2n-(NEQ( 0 Rec.Com.DQEmax)Re(.!ConK ) SNR gain (21) (NEQmax}Donor 76

The of the doubling(2) numerator value in equation 21 Is due to the

fact that because the donor 1s a double sided emulsion, In actuality two receiver-composites can be had for the price of one donor exposure. the Substituting appropriate values Into equation 21, one obtains for n

io7-55 " 6-88 = = n 5.62 -*. 5

and for . SNRgain

2-5X013) SNRgaiV 1.27 .08

Therefore by using two receiver film sheets for each of five seperate and lesser exposures at DQEmax of the receiver-composite, a 27% increase in SNR is achieved over of the NEQ ,w the donor. max To be sure, the method of actually registering Images as

suggested here is probably cumbersome and unfeasible in most working environments. However, the intention here 1s not so much of a practical nature as much as demonstrating that when working at the limits of detection the type principles advocated here are certainly plausible. It is up to the user to translate these principles into practice for the particular needs at hand. 77

5. CONCLUSIONS 78

This research effort has been concerned with the measurement and evaluation of a thiourea S-35 nuclide autoradiographic image enhancement process; especially as It applies to medical diagnostic Imagery. Specific attention was paid to that enhancement scheme

Incorporating a subproportlonal potassium ferrlcyanide bleach In the activating solution. This was chosen largely due to the encouraging quantitative and qualitative results with this process by previous 9-12 workers .A block diagram of the autoradiographic process studied here 1s given 1n figure 22.

One of the Important items to come out of this past work was unanimous reports of Increased visual detection 1n the receiver-composite generated images when compared to those of the donor. By quantifying the signal -to-no1se ratio (SNR) properties of this autoradiographic process, and comparing their values at the donor and receiver-composite stages, 1t was hoped that this reasearch could lend some insight into the reasons for the reported visual detection

Increases. The SNR metrics chosen for this quantification were

Detective Quantum Efficiency (DQE) and Noise Equivalent Quanta(NEQ). It was shown how DQE Is important for most efficiently detecting quanta, while NEQ 1s Important for detecting a signal with maximum likelihood.

For this work DQE and NEQ were defined as a function of both exposure(q), and rotationally symmetric spatial frequency(w) as:

n9m*i2W<,2("TF(w))2 DQE(q.w) - q-W(q.w)

and

NEQ(q,w) = DQE(q.w). q

= the characteristic curve where - Differential gamma of MTF * Modulation transfer function

W = Wiener spectrum 79

Quantifying tyq) and q was done through the donor and receiver-composite characteristic curves Illustrated In figure 23.

From these curves 1t was shown that, in addition to an approximate 2 stop speed Increase, the receiver-composite also exhibited a greater maximum gamma than that of the donor( 5.8 vs. 4.2). Because of the receiver-composite's lower Dmax however, the input exposure latitude for 1t was limited to about half that of the donor.

In quantifying the MTFs, 1t was shown that the donor's 40 equivalent bandwidth was 50.1 greater than for the receiver-composite. A comparison of these MTFs can be found 1n figure

24. It was also shown that, in analogy, the changes In MTF 1n going

"medium" from the donor to receiver-composite are akin to going from a

"fast" to a radiographic screen/film system. The graphs supporting this are given in figure 25.

In measuring the final contributing parameter, Wiener spectrum, 1t was found that while both donor and receiver-composite

Wiener spectra followed the general shape of Rossman's model, neither 2 of the spectra fell off with MTF , as predicted. This Indicated sources of noise that were not influenced by the MTF of the processes. It was also shown that for equal densities less than 1.2, the low frequency (I.e.,. 40 mm"1) Wiener spectra values were generally an order of magnitude higher 1n the receiver-composite than In the donor.

Figure 26 shows this, along with Illustrating that for equal exposures, these same receiver-composite Wiener spectrum values were two orders of magnitude greater than for the donor.

Finally, by mathematically joining the above metrics 1t was shown that the donor according to the DQE and NEQ equations,

of the receiver-composite 50.%. DQE of .30 exceeded that by

max. . . .. - .. _2 . of Similarly, the donor NEQmax of .08 um exceeded that the Illustrated 1n figures receiver-composite by 350.%. These results are donor DQE and continued 27 and 28. It was further shown that the NEQ

even on an equi-exposure to exceed that of the receiver-composite

reason this was due to the basis. It was felt that the for primarllly

of the receiver-composite largely Increased Wiener spectrum values 80

step. From a qualitative viewpoint, It was speculated that the mismatch between lower receiver-composite NEQ and reported visual detection Increases was due to contributions of the human visual process that are not strictly predicated on SNR analyses.

Quantitatively, 1t was pointed out that the mismatch may also be due to insufficient data collection over the exposure sample space. In looking to the future, verification of the results just presented is strongly urged. In so doing however, particular attention should be paid to both an adequate exposure sample space, and error budgets on the Individual components leading to the DQE and NEQ metrics. There are, no doubt, many operator error Influences

confounded in these results that cannot be strictly accounted for.

Perhaps in reading this text, future workers may benefit by avoiding

methods. It is also any pitfalls they deem present 1n the experimental a suggested that a specific experimental effort be directed towards

donor and receiver-composite. This study of the noise transfer between of the effort should certainly help 1n gaining an understanding

noted 1n the receiver-composite as alarming Wiener spectrum Increases future studies. well as acting as a springboard for 81

r ~1

PECEIVEP SCREEN FILM

I DEVELOP l i

1 DONOr. 1T.AGE l Ponor ige Irna Cha in J i

CONTACT ACTIVATE

'

RECEIVER COMPOSITE

TMiGF

Receiver- compos ite Image Cha in

Figure 21: Block Diagram defining Donor (dash) and Receiver-Composite (bold solid) stages. 82

S;

s

Ads. Log Exposure 7 photons /so. cm. J

Figure 22: Characteristic Curves for

different stages of the Auto

radiographic system tested 83

to E CU 1 +-> i. +x 10 CU LO >, i. > ro to CO 407 r t- m _ o u. CU E y- i n r r~ u. u E r- 1 i CU ro E ll- E i- cc o 0*9 ^ ^ *4v E .. CL Ll_ i o C CL >> c >> cu U_ E Jl o ro yx CU c OJ OJ L. li 0"9 | S- .c o QJ u o -> to L. CO c r- O ft a o 3 "O OJ OJ jl o cu L> T3 OJ -0-i7 -Z to cu Ol D. t- Li. CL ai (/I \ a. o to i/> z / 1 E c E 3 4-> r1 o cu 3 0" r- cn -o to +J (D OJ // r- r -o a. / s- to cu ro O E 1 CL CL -4 / . O'Z -o 1 ? EE o O c 1 CJ CJ ro 1 *' O'l

ta-

CSJ

cu > JL. -a. S- o 3 CO CT

uo.LiBinpow

s- o

to c o r"

-4-> s- u a> to c > cu 3 t- CD U_ CU ro u +j S- cu to CU Oi t- to TD "O C C x- ro ro x- s- o h- '- to 4w* -C C tO o ro CU - "D yx 4-> r ro to f u O 3 O CL XJ C E o o o s o CJ

## CO CM

cu i. 3 CD uofwww 84

0) > o

<.ot;

-.3.0

-5.0

.4.0

Absolute Log Exposure(photons/cm')

Receiver Figure 25: W(.4) for Donor (solid) and Composite (dash) compared to respective characteristic curves. Noise power right on left ordinate & Density on ordinate. 85

Absolute Log Exposure (photons/cm )

Figure 26: Donor DQE (solid) and NEQ (single dash]

curves; @ .40 mm"1.. Relative Density characteristic curve for comparison. 86

^ "NNEQ / \ Cr o / d a x

20' DQE / , 3 \ y'jJjsL* D. E O /X\ // /

-/! 1 / * i a / %X-75 s

^^

t i i i

Absolute Log Exposure (photons/cm2)

Figure 27: Receiver Composite DQE (solid) & NEQ Relative (single dash) curves @ .40 mm"1. Density characteristic curve for comparison. 87

6. REFERENCES

1. Anonymous, Stein Der Weisen, 35, 340(1906). 2. H.E.Wheeler, N.L.Wheeler, and C.W.Durieux, U.S. Patent #2,780,732(1957).

3. M.Thackray.et.al., Int.J. Appl. Radiat. Isotopes, 23, 79(1972). 4. E. Ostroff,J. Photoscience, 13, 213(1965).

5. M.Thackray.Austr. Atomic Ener.Comm. ,#AAEC/E317(1974).

6. a)B. Askins, Science, 199, 684, ( 1978). b)B. Askins,U.S. Patent #4,101,780(1978).

7. R.Pettijohn.and C.Leung, SRI International ,Proj.#PYU8468( 1980).

8. T.H.James, and W.Vanselow,J. Phys. Chem., 57, 725(1953).

9. D.Dempster,Master Thesis, R.I.T. ,SPAS(1978).

10. D.Vachon .Master Thesis, R. I. T.,SPAS(1979).

11. L.Wheaton, R.I.T., personal communicat1ons(l980).

12. L. Wheaton .Master Thesis, R. I. T.,SPAS(1980). 13. A. Rose.J. Soc.Mot. Picture. Eng.,47, 273(1946).

14. R.C.Jones.J. Opt. Soc. Amer., 39, 327(1949).

15. P.B.Fellgett,J.0pt.Soc.Amer.,39,970,(1949). b)R.Shaw,J. Phot. 16. a)R.Shaw,J.Phot. Sci., 15, 78( 1967). Sci., 16, 170, (1968).

17. H.J.Zweig.Phot.Sci.4 Eng. ,8,305(1964). 2389(1969). 18. G. R. Bird,et.al., Appl .Opt. ,8, 19. J. C.Marchant.J. Opt. Soc. Amer., 54, 798(1964). Science.Academic Press, 28(1974). 20. J.C. Dainty, and R.Shaw, Image

21. Reference 20, page 156.

22. Reference 20, page 312.

23. R.Shaw.J. Phot. Sci., 17, 155(1969). Chicago. 213(1962). 24. w. A. Baum.Astron. Tech., Univ. Press,

25. A.Guttman.Phot.Sci.4 Eng. ,12,146(1968). Astron.Soc.Conf.on Astron.Opt. 26. R.L.Porteous.and R.Shaw, Royal

(1967). 88

27. H.E.Johns, and J. R.Cunningham, The Physics of Radiology, Charles C. Thomas, 735(1977). 28. R.E. Swing, Opt. Eng., 15, 559(1976). 29. R.L. Lamberts,J. Opt. Soc. Amer., 51, 982(1961). 30. R.Porth,Master Thesis, R. I. T.,SPAS(1984).

31. and G.Sanderson, H.Cleare,Phot.Sci.4 Eng. ,18,251(1974). 32. P. Burns, and B.Levine, Xerox Internal Report #X2013529(1981). 33. Reference 20, page 276. 34. E.Trabka,J. Opt. Soc. Amer., 59, 662(1964). 35. K. Rossman, Amer. J. Roent., 90,863(1963).

36. C. Dainty, Univ. Roch., personal communications(1982).

37. D.Plewes, Univ. Roch., personal communicat1ons(l98l). 38. K.Doi.U.S.Dept.of H.H.S.,Publ .#FDA 82-8187(1982).

39. K. Taylor,et.al.,S. P. I.E. Conf.on Appl. of Opt. Inst. in Medicine VII, 173, 307(1979).

40. R.Bracewell ,The Fourier Transform 4 Its Applications, McGraw-Hill, 151(1978). 41. K. Rossman, J. Opt. Soc. Amer., 52, 774 (1962). 42. E.W.Selwyn, Photogr.J., 75, 571(1935).

43. R.Wagner, and E.Muntz.S.P. I.E. Conf.on Appl. of Opt. Inst. in Medicine VII, 173, 122(1979).

44. R.Wagner, Phot. Sci. 4 Eng. ,21,252(1977).

45. P.Bevington.Data Reduction and Error Analysis for the Physical

Sciences, McGraw-Hill,64(1969).

46. W.Moore, Kodak Res. Lab. .personal communication(1984).

47. R.Shaw, Phot. Sci.* Eng. ,17,495(1973).

48. D. Goodenough, Phot. Sci. 4 Eng. ,21,262(1977). 49. R.Halmshaw,J. Phot. Sci., 19, 167(1971).

50. Reference 20, page 307.

51. Reference 20, page 162. 52. R.Shaw, J. Phot. Sci., 20, 175(1972).

53. W.Smith,Modern Optical Engineering, McGraw-Hill ,290(1966).

54. J.Jakubowski.Xerox Corp. .personal communication (1980). 89

7. APPENDICES 90

7.1 APPENDIX A

EQUIPMENT, PROCESSING, & MEASUREMENT PARAMETERS 91

LIST OF MAJOR EQUIPMENT

Special Bracke-Seib X-Ray Machine 70 KVP, 105 Volt Primary, Kodak Research Laboratories. '

Kodak XG Radiographic Film

Kodak NMC Nuclear Medicine Film

Kodak X-omatic Regular Screens #688250K (front); #699251K (back)

Macbeth TD-504 Densitometer

Kodak RP-X-OMAT Film Processor

Kiethley Model 35020 dosimeter,Model 96020A ion chamber

Zeiss SMP05 microdensitometer

Inverse Square Exposure Bench, Kodak Research Laboratories 92

j

Wo-fJectrori yoJts

for Figure Al: Spectral Power Distribution

nominal 70Kvp X-Ray source with

copper & 1 mm Aluminum .5 mm 93

ACTIVATING SOLUTION PROCESSING

Solution A

25 ml of .4% NaOH Solution

Equivalent of .5 m Ci of S-35

10 ml of .15% S-32 thiourea

Solution B

150 ml of .625% Potassium Ferricyanide solution

Immediately before processing mix equal portions of solutions A & B, and adjust temperature to 70F and pH to 12.5.

1) Agitate donor strips in A/B mixture for 30 minutes

2) Wash strips for 1 minute 3) Dry strips 4) Contact donor tube side to NMC film emulsion for 1.5 hrs 5) Process NMC film in X-OMAT Processor 94

CAMERA

-

SIGNAL

SLIT OR APERTURE

CHOPPER LAMP -lf* fl

NDA REF n an --D H--D-* LJ l*J

SMP05 Figure A2: Schematic Diagram of Zeiss

microdensitometer used for densit 54 ometer measurements for experiment 95

COMMON CONDITIONS FOR MICRODENSITOMETRY

.08 N.A. efflux objective

.60 N.A. influx objective

14X influx magnification

40mm~ n0 = assumed diffraction limited optics effective scanning slit dimensions

25um x 700um

sampling interval = 12.5um

image scan, overfill mode

3X overillumination of scanning slit in width (25um) dimension

3 reads per sample 96

7.2 APPENDIX B

CALCULATIONS & CURVE FITS 97

EXAMPLE CALCULATION FOR PHOTON FLUENCE

CALCULATION FROM ROENTGENS.27

From reference 27 we have

# photons 86.94

2 -9 cm "roentgen 1.59-10 #Kev

where ju = Mass attenuation coefficient of air

# Kev = Number of Kev associated with the spectral source

Since u is a function of Kev and likewise, the weighting of Kev is dependent on the spectral energy distribution of the source, a summation over the broadband source must be done. This source distribution is given in Appendix A. Therefore the working equation to arrive at the LHS of the above equation becomes

72

86.94 1

YV-) -9 L u(i) 1.59*10 i~^20

..th where t|(i) = Relative power associated with the i Kev

;th u(i) = Mass attenuation coefficient at the i Kev

i = Kev

calibrated The result of this summation was then multiplied by the measure of 1.204 mi Hi roentgens to arrive at a photon fluence of

107,49 at a density of 1.2 above base for the donor. 98

CALCULATIONS FOR MICRODENSITOMETER DEPTH-OF-FOCUS, LINEARITY, AND EFFECTIVE INCOHERENCE CONDITIONS

DEPTH-OF-FOCUS

51 From Smith the depth-of- focus, L , for diffraction limited systems is

A = (N.A.)2 (N.A.)2 2 N N

for r- = 550 nm N = 1.5 ( emulsion index of refraction) A = 230 um total for donor film

The required numerical aperture would have to be ^ .040. This low a numerical aperture being unavailable the single

emulsion depth was only considered. It was only 40 pm deep.

Therefore, a relaxation of the numerical aperture to * .096

was calculated. An available .08 N.A. efflux objective was used.

This being the lowest numerical aperture objective available, an

over fill mode was predicated.

LINEARITY

28 Using Swing's nomenclature,

Maximum frequency of interest = nQ= 40. mm

= Cutoff frequency of efflux = cr 290. optics

The linearity conditions are

^ - e> i + 1.14 (To

N.A.,. where influx = N'A'efflux

N-A--jnfiux= Therefore using .60 99

.6

= = 6 7 . 5 > 1 . 14

.08

Therefore the linearity requirements were satisfied.

EFFECTIVE INCOHERENCE

Effective scanning slit width calculation

In order to prefilter for 40. mm with a rectangular slit, a

= = .025 25 micrometer slit width was used 40.

Effective Incoherence

p> 4 + Q( nQ +

. width of microdensitometer source slit where p = coherence interval of source

For this experiment

1050 um ., p = - i\c. 25 um

+ and 42 > 4 Q( .330 )

Solving for Q Q < 115.15 micrometers

= on the sample where Q reduced image of the source aperture Therefore the influx magnification, Minf-ux must satisfy

microdensitometer source slit M. ., width of influx = Q

or micrometers 1050 - M N " a \o influx ^ 115.15 micrometers 100

Since

14 > 9.12

the effective incoherence conditions were then met with the .60 N.A. influx objective using an auxiliary ocular to give the total 14x magnification. 101

6.00.

4.00..

Donor

9.00..

Receiver- 1 Composite 2.00

1.00..

0.00

Ads. Log Exposure fphotons / sg. cm. J

Figure Bl: Comparison of raw data with

characteristic curve fits

- Donor RMSE .0178 Receiver-Composite RMSE =.0287 Tube & non-tube RMSE =.0185 102

3598

;^vvX,.

3009 * mmU

2599

2999

1599

pjV'^'.'XAii.j,

v_ 1900 i i i

0.0 1.9 2.0 3.0 4.0

DISTANCE

Figure B2: Comparison of raw data with

profile. cubic spline fit of edge

Knots indicated by circles. 103

fll

o CO

-4- l OJ "T" 4- l to O E c l/J B cu **"' >> o -o yx o. E >> s- to o u o c (J c c cu I OJ o T3 S- 3 XJ OJ CT OJ > CU T3 +J S- H- OJ cu -o to o r o x- OJ CO Q. cc rO r E VII o +J p o ro CD 1 Q. C S- CO x- vu LQ >

S- OJ o o q- - J OJ ttj S- to 9 +J 9 9 X> x- c M- ro

E , . 3 4-> S- V(- +-> OJ o x- cu .4" D. OJ ru to to CS ro s- J2 OJ c CU cu > X" o OJ 3: XI to ro (0

OJ .o ^^ ^~ CO H o. VO OJ 1 E . > E ro O E X M-. J3 LU O ro

>> .. o CO c OQ OJ =J OJ O" S- OJ 3 s- O

ro

4-> fO Q. CO 104

h + b

+ .8h b

.6h + b ..

.4h + b ..

+ ,2h b ..

q - ---?-- + W(w) = h( 1 ( )2) b max

donor & Figure B4: Family of Curves used for

receiver-composite Wiener spectrum

fits. 105

DERIVATION OF COMPOSITE SNR

FOR REGISTERED IMAGES

+ h let S. = Signal of the i component

a. = Noise of the i component

S. + + + , S, Sn Vm I ,, ,2 -2 . , \2J/2 N'comp +, , + ((c^) (a2) . . . (an) )

for equal signals and noise

nS r~ ,S\ _ _ " S_ Vcomp (nc2-l/2 a

^comp = ^ (f}

2 j2 s Wcomp = n ^

2 s () = n (NEQ(q)) ^Nxomp

(DQEmax))1/2 Wcomp = (n NEQ

that the individual noise The assumptions involved are additive in of each other and truly components are independent

nature. 106

7.3 APPENDIX C

SUPPLEMENTAL GRAPHS 107

LIST OF FIGURES

FOR APPENDIX C

Description Figure #

Characteristic curves in roentgens CI 9 Characteristic curves in ergs/cm C2

MTFs on log-log coordinates C3 Gamma vs. density curves C4 Donor W.S. vs. log exposure 4 frequency C5 Donor W.S. vs. density 4 frequency C6 Receiver-comp. W.S. vs. log exposure 4 frequency C7 Receiver-comp. W.S. vs. density 4 frequency C8 Donor DQE vs. log exposure 4 frequency C9 Donor DQE vs. density 4 frequency CIO Receiver-comp. DQE vs. log exposure 4 frequency Cll Receiver-comp. DQE vs. density 4 frequency C12 Donor NEQ vs. log exposure 4 frequency C13 Donor NEQ vs. density 4 frequency C14 Receiver-comp. NEQ vs. log exposure 4 frequency C15 Receiver-comp. NEQ vs. density 4 frequency C16 C17 Tube 4 non-tube side MTFs C18 Characteristic curve comparisons to ref. 38 C19 Typical screen/film Wiener spectra from ref. 38 020 MTF comparisons to ref. 38 108

6.00 _

Oi

4.00..

3.00 ..

Receiver- I 2.00 .. Composite

1.00

0.00.

ADs. Log Exposure f roentgens J

Figure CI: Characteristic Curves of

different stages in roentgens 109

B.OO,.

in ti

4.00..

V4. 3.00..

""1

Receiver- I 2.00.. Composite

Ci

^ 0.00

ADs. Log Exposure 7 ergs / sg. cm. J

Figure C2: Characteristic curves at

ergs/cm' different stages in 110

0.08

Spatial Frequency f cycJes X mm. J

Figure C3: MTFs on log-log coordinates for

Donor and Receiver-Composite Ill

6.00,

5.00. Receiver-Composite

4.00.

\ Donor

1 i 1 1 I I I 1 1 H

lO

Macro Diffuse Density fatore Aase J

Figure C4: Gamma vs. Macro-Diffuse Density

for Receiver-Composite & Donor 112

7.80

7.70

N

\ ! I 1 I

"4J

SpatJaJ Frequency f cycJes / mm. J

Figure C5: Donor Wiener spectrum contour plots vs.

log exposure & spatial frequency 113

1 I I

2) o f* o ft 5 8 8 8 8 8 8 8 o o d o ^ ID CD r.

Spatja] Frequency ( cycJes / mm. J

Figure C6: Donor Wiener spectrum contour plots vs.

Macro-diffuse density and spatial frequency 114

7.30,.

\ 1

|

W1 0 I** fi ft S 8 8 8 8 8 8 3 d o d o o *i V id n d n

SpatJaJ Frequency 7 cycJes / mmj

Figure C7: Receiver-Composite Wiener spectrum

exposure & contour plots vs. log

spatial frequency 115

1 i I

SpatJaJ Frequency 7 cycJes A mm. J

Figure C8: Receiver-Composite Wiener spectrum

contour plots vs. Macro-diffuse density

& spatial frequency 116

\ 1

|

VI

8 8 888888

SpatJaJ Frequency 7 cycJes / mm. J

Figure C9: Donor DQE contour plots vs. log

exposure & spatial frequency 117

8 a

I 1 I

8 8 8 8 8 8 8

SpatJaJ Frequency 7 cycJes / mm. J

Figure CIO: Donor DQE contour plots vs.

Macro-diffuse density & spatial frequency 118

7.30

7.ao^

S 7W

* \ 7.00 1 e.Bo

I 8.80.. |

8.70

NI

8.BO..

8. BO 8 8 889888 cu cu cu cu cu n

SpatJaJ Frequency 7 cycJes / mmJ

Figure Cll: Receiver-Composite DQE contour plots

vs. log exposure & spatial frequency 119

1

1

S g S 8 cu oj oi

Spatial Frequency 7 cycJes / mm. J

plots Figure C12: Receiver-Composite DQE contour

spatial vs. Macro-diffuse density &

frequency 120

SpatiaJ Frequency 7 cycJes / mm. J

NEQ(um~ Figure C13: Donor ) contour plots vs.

log exposure & spatial frequency 121

i

I 1

SpatJaJ Frequency 7 cycJes / mm. J

NEQ(um~ Figure C14: Donor ) contour plots vs. Macro-diffuse density & spatial frequency 122

7.30

7.20

7.10..

\ 7.00 1 Vl I 6. 80

I B.80 I

8.70 . .

VI

8.80..

B.50 8 S 8 8 8

i w cu cu cu cu m

SpatJaJ Frequency 7 cycJes / mm. J

Figure C15: Receiver-Composite ) contour

plots vs. log exposure and spatial frequency 123

I 1

i i i i i i 8 8 8 8 9 8 8 8

w < cu cu cu cu cu en

SpatJaJ Frequency 7 cycJes / mm. 7

_2 Figure C16: Receiver-Composite NEQ(um ) contour

plots vs. Macro-diffuse density and

spatial frequency 124

OJ -o

OJ jO 3 f- I C o

oS

O)

3

C OJ OJ s +J s- OJ o Nonvinaow X) c o C Q o tO S- i- o S_ V|_ fO Q. to E O fcf o s:

|4- H CJ

cu S- 3 CD

Nonvinaow 125

5.00 _

ADs. Log Exposure 7 roentgens J

Figure C18: Comparison of relative characteristic

curve shapes between this experiment

(solid) and results of reference 38 (dash) for Donor. 126

ICT "I I II I T I I l-l

3.o-

< ,PARSPEED/ XRP (U.C.) cc /HI-PLUS/XfW (U.C.) 1 DETAIL /XRP (U.C.) cc W I0"t o Lvl inivi**n.nM.\ 5 + MI-M.US/IHP ll.H.H.) OCTAIL/XKPII.ItM.)

i i i i i i i i i i o.i 0.2 0.9 1.0 2 10 SPATIAL FREQUENCY (CYCLES/MM)

Fiqure C19: Typical absolute Wiener spectrum 2 2 values in Macro D mm for screen/

film radiographic systems. (from

reference 38) 127

CO Li- CO h- 00 Li. s. CO

OJ 1 XX s E r ^~ to E .r- O ^~ Li. CL 'r- ^^ E U. C O ^4. OJ CJ C OJ s- u_ 1 OJ S- 0J o 1 s- OJ o > 0J s: OJ CO -0*8 > o 0J i- r vo -o CJ o CU w 0J ro c u "D cu o o OJ OJ ex 0) o cc OJ to C" Q. +j Q. to o o to - >> OJ OJ E 1/ x-l o to S- S- r 3 O +- 3 3 4 [1 E o yx c to to to -D E Q cu ro ro ro OJ 0J OJ CU Li. s: 0*9 4_ s- s: s: = r u to A 1 c CJ o CU E iI 1/ to 4-> i

/'" I 0'9 | 5_ to m- CT ro o 1 OJ Q. Q. -U // S- E E to o O ro // CJ O 1- 0'* // o C\J II ro o a. LO OJ Ai J- o-e 3 // cn /

x^ ? .- 0*2 X / 'm s ^ -" 0*1 ^x xV"

j^*^^ ^?<*'

j 4-1 ,i,. ,. ,

o o o o "3- CO VO C\J

uo.uBLnpow 128

7.4 APPENDIX D

COMPUTER PROGRAMS 129

SUBROUTINE SPL2Z(DATAX,DATAY,ND,XNOT,NK,Y,M,RMSE,AVABE) C C SPL2Z IS A FORTRAN CALLABLE SUBROUTINE WHICH CALCULATES THE C LEAST SQUARE CUBIC SPLINE SUBJECT TO THE CONSTRAINT THAT THE C SLOPE MUST BE ZERO AT THE ENDPOINTS. C XNOT IS THE VECTOR OF KNOT LOCATIONS C DATAX AND DATAY ARE THE VECTORS OF THE ABSCISSA AND ORDINATE C VALUES OF THE DATA. C MAXIMUM NUMBER OF DATA POINTS-400 C MAXIMUM NUMBER OF KNOTS-7

DIMENSION DATAX( 1 ) ,DATAY( 1 ) ,XNOT( 1 ) ,M( 1) ,Y{ 1) DIMENSION H(6),A(7,7),B(7,7),C(7,7) DIMENSION AINV(49) DIMENSION ZZ(2800) DOUBLE PRECISION AINV.D REAL M,H C C CHECK ORDER OF KNOTS AND REORDER IF NECESSARY C 5 DO 10 I=1,NK-1 IF (XN0T(I+1).GE.XN0T(I)) GO TO 10 E=XN0T(I+1) XN0T(I+1)=XN0T(I) XNOT(I)=E GO TO 5 10 CONTINUE C C SET ELEMENTS OF MATRICIES A,B,4 C EQUAL TO ZERO C DO 20 1=1, NK DO 20 J=1,NK 20 A(I,J)=B(I,J)=C(I,J)=0.0 C C CREATE VECTOR H C DO 30 I=1,NK-1 30 H(I)=XN0T(I+1)-XN0T(I) C C CREATE MATRIX A C DO 40 I=1,NK-1

1+1 1+1 1+1 , I )=H( I ) A( I , 1+1 >=A( , )=A( 40 A(I,I)=(A(I,I)+H(I))*2. A(NK,NK)=A(NK,NK)*2. C C CONVERT MATRIX A INTO A VECTOR AINV C K=0 DO 50 1=1, NK DO 50 J=1,NK K=K+1 50 AINV(K)=A(I,J) 130

C C INVERT MATRIX A C CALL DMINV(AINV,NK,D,M,Y) IF(D.EQ.0.D0)TYPE "*** MATRIX A IS SINGULAR ***" C C CREATE MATRIX B C DO 60 I=1,NK-1 B(I,I+1)=B(I+1,I+1)=B(I+1,I)=6./H(I) 60 B(I,I)=(B(I,I)+6./H(I))*(-l.) B(NK,NK)=B(NK,NK)*(-1.) C C CREATE MATRIX C BY POST MULTIPLYING AINV BY B C DO 70 1=1, NK DO 70 J=1,NK D=O.DO DO 65 K=1,NK 65 D=D+AINV(I+(K-1)*NK)*B(K,J) 70 C(I,J)=D C C ABCSISSA VALUES ARE ASSUMED TO BE IN ASCENDING ORDER AT THIS POINT C C SET ELEMENTS OF MATRIX Z EQUAL TO ZERO C DO 90 I=1,NK*ND 90 ZZ(I)=0.0 C C CREATE MATRIX Z FROM DATAX.H, 4 C C K=l DO 100 1=1, ND NQ=(NK-1)*ND IF(DATAX(I).LT.XN0T(1)) GO TO 101 IF(DATAX(I).GE.XNOT(NK)) GO TO 102 92 IF(XNOT(K).LE.DATAX(I).AND.DATAX(I).LT.XNOT(K+D) GO TO 93 K=K+1 GO TO 92 93 DU=XN0T(K+1)-DATAX(I) DL=DATAX(I)-XNOT(K) Wl=DU**3/(6.*H(K))-DU*H(K)/6. W2=DL**3/(6.*H(K))-DL*H(K)/6. W3=DL/H(K) W4=DU/H(K) DO 95 J=1,NK NX=(J-1)*ND 95 ZZ(NX+I)=W1*C(K,J)+W2*C(K+1,J) NZ=(K-1)*ND ZZ(NZ+I)=ZZ(NZ+I)+W4 NW=K*ND ZZ(NW+I)=ZZ(NW+I)+W3 131

GO TO 100 101 ZZ(I)=1.0 GO TO 100 102 ZZ(NQ+I)=1.0 100 CONTINUE C C CALCULATE THE LEAST SQUARES ESTIMATE OF VECTOR Y C CALL LINREG(ZZ,DATAY,Y,NK,ND) C C CALCULATE RECONSTRUCTED DATA VALUES RESIDUALS, RMSE C AND AVERAGE ABSOLUTE ERROR. RMSE=AVABE=ERRSUM=0.0 DO 110 1=1, ND SUM=0.0 DO 105 J=1,NK NU=(J-1)*ND 105 SUM=SUM+ZZ(NU+I)*Y(J) RES=SUM-DATAY(I) ERRSUM=ERRSUM+RES RMSE=RMSE+RES**2 110 AVABE=AVABE+ABS(RES) RMSE=SQRT(RMSE/ND) AVABE=AVABE/ND C C CALCULATE VECTOR M FROM M=CY C DO 120 1=1, NK SUM=0.0 DO 115 J=1,NK 115 SUM=SUM+C(I,J)*Y(J) 120 M(I)=SUM RETURN END 132

SUBROUTINE SPLVAL(X,S,XNOT,Y,M,MK,K) DIMENSION XNOT(NK),Y(NK),M(NK) REAL M IF(X.LT.XNOT(l)) GO TO 101 IF(X.GE.XNOT(NK)) GO TO 102 10 IF(XN0T(K).LE.X.AND.X.LT.XN0T(K+1)) GO TO 20 K=K+1 GO TO 10 20 DU=XN0T(K+1)-X DL=X-XNOT(K) XH=XN0T(K+1)-XN0T(K) DIV=6.*XH S=(DU**3*M(K)+DL**3*M(K+1)+DL*(6.*Y(K+1)-M(K+1)*XH*XH) 1 +DU*(6.*Y(K)-M(K)*XH*XH))/DIV GO TO 100 101 S=Y(1) GO TO 100 102 S=Y(NK) GO TO 100 100 CONTINUE RETURN END 133

SUBROUTINE SPLFTZ(F,TM,TP,TR,TI,Y,Q,XNOT,NK) DIMENSION Y(NK),XNOT(NK),Q(NK) IF(F.EQ.O.O) GO TO 31 PI=3. 141592653589793284626433832795 10 W=2*PI*F W2=W*W W3=W*W*W ARGA=W*XN0T(1) ARGB=W*XNOT(NK) CA=COS(ARGA) CB=COS(ARGB) SA=SIN(ARGA) SB=SIN(ARGB) SUMR=(Q(NK)*CB-Q(1)*CA)/W2 SUMI=(Q(NK)*SB-Q(l)*SA)/(-W2) L=NK-1 DO 20 1=1, L SUMR=SUMR-(Q( 1+1 )-Q( I ) )*(SIN(W*XNOT( 1+1 ) )-SIN(W*XNOT( I) ) )/ 1 (W3*(XN0T(I+1)-XN0T(I))) SUMI=SUMI-(Q( 1+1 )-Q( I ) )*(COS(W*XNOT( 1+1) )-C0S(W*XN0T( I) ) )/ 1 (W3*(XN0T(I+1)-XN0T(I))) 20 CONTINUE TR=SUMR/(Y(NK)-Y(D) TI=SUMI/(Y(NK)-Y(D) TM=SQRT(TR*TR+TI*TI) TP=ATAN2(TI,TR) GO TO 30 31 TM=TR=1.0 TI=TP=0.0 30 RETURN END 134

SUBROUTINE LINREG(X,Y,B,NC,NR) DOUBLE PRECISION SUM.XPX DIMENSION B(NC),Y(NR),X(NR,NC) DIMENSION XPX(49),XPY(7),LL(7),MM(7) C C X IS A MATRIX OF PREDICTORS, DIMENSIONED (NR.NC) C Y IS A VECTOR OF RESPONSES C B IS A VECTOR OF LEAST SQUARES COEFFICIENTS C C FORM X.X MATRIX C M=0 DO 10 J=1,NC DO 10 K=1,NC SUM=O.DO DO 9 1=1, NR 9 SUM=SUM+X(I,J)*X(I,K) M=M+1 10 XPX(M)=SUM C C INVERT X.X MATRIX USING IBM SSP DOUBLE PRECISION MINV C CALL DMINV(XPX,NC,SUM,LL,MM) C C REPORT SINGULAR X.X MATRIX C IF(SUM.EQ.O.DO) TYPE. ***XPX MATRIX IS SINGULAR*** C C FORM X.Y MATRIX DO 14 J=1,NC SUM=O.DO DO 15 1=1, NR 15 SUM=SUM+X(I,J)*Y(I) 14 XPY(J)=SUM C C CALCULATE B VECTOR C M=0 DO 5 1=1, NC SUM=O.DO DO 6 J=1,NC M=M+1 6 SUM=SUM+XPX(M)*XPY(J) 5 B(I)=SUM RETURN END 135

SUBROUTINE DMINV(A,N,D,L,M) DIMENSION A(1),L(1),M(1) DOUBLE PRECISION A,D,BIGA,HOLD D=l. NK=-N DO 80 K=1,N NK=NK+N L(K)=K M(K)=K KK=NK+K BIGA=A(KK) DO 20 J=K,N IZ=N*(J-1) DO 20 I=K,N IJ=IZ+I 10 IF(DABS(BIGA)-DABS(A(IJ))) 15,20,20 15 BIGA=A(IJ) L(K)=I M(K)=J 20 CONTINUE J=L(K) IF(J-K) 35,35,25 25 KI=K-N DO 30 1=1, N KI=KI+N H0LD=-A(KI) JI=KI-K+J A(KI)=A(JI) 30 A(JI)=HOLD 35 I=M(K) IF(I-K) 45,45,38 38 JP=N*(I-1) DO 40 J=1,N JK=NK+J JI=JP+J HOLD=-A(JK) A(JK)=A(JI) 40 A(JI)=HOLD 45 IF(BIGA) 48,46,48 46 D=O.DO RETURN 48 DO 55 1=1, N IF(I-K) 50,55,50 50 IK=NK+I A(IK)=A(IK)/(-BIGA) 55 CONTINUE DO 65 1=1, N IK=NK+I HOLD=A(IK) IJ=I-N DO 65 J=1,N IJ=IJ+N 136

IF(I-K) 60,65,60 60 IF(J-K) 62,65,62 62 KJ=IJ-I+K A(IJ)=HOLD*A(KJ)+A(IJ) 65 CONTINUE KJ=K-N DO 75 J=1,N KJ=KJ+N IF(J-K) 70,75,70 70 A(KJ)=A(KJ)/BIGA 75 CONTINUE D=D*BIGA A(KK)=1./BIGA 80 CONTINUE K=N 100 K=K-1 IF(K) 150,150,105 105 I=L(K) IF(I-K) 120,120,108 108 JQ=N*(K-1) JR=N*(I-1) DO 110 J=1,N JK=JQ+J HOLD=A(JK) JI=JR+J A(JK)=-A(JI) 110 A(JI)=HOLD 120 J=M(K) IF(J-K) 100,100,125 125 KI=K-N DO 130 1=1, N KI=KI+N HOLD=A(KI) JI=KI-K+J A(KI)=-A(JI) 130 A(JI)=HOLD GO TO 100 150 RETURN 137

C CLAUDE REAL DATA(52,200),ADATA(100,2),TRAN(200),W0RK(202) C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CC c C (NENS.NPTS) (NPTS/2,2) (NPTS) ( ? ) C

C SET INITIAL CONDITIONS FOR SLIT LENGTH(EL) ,SLIT WIDTH(SLWI), VALUE OF C PI(PI), NUMERICAL APERTURE (AN) .SAMPLING FREQUENCY(SMDS) ,

NUMBER .POINTS C OF ENSEMBLES( NEWS) PER ENSEMBLE(NPTS) , MEASUREMENT

C WAVELENGTH (WAVE), MACRO BASE DENSITY(DMACB) , SLOPE F C MACRO DENSITY(SMAMIC), 4 A CONSTANT FOR MICRO TO MACRO C DENSITY CONVERSION(CMAMIC). ALL DISTANCES ARE IN MICRONS. C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CC c

DATA EL, SLWI, PI, AN, SMDS, NENS.NPTS, WAVE, DMACB,SMAMIC,CMAMIC/701. , 125. 5, 3. 1415926535897932384,. 08, 12. 5, 52, 200,. 550,. 14,. 885,. 0297/ READ(113,10)((DATA(I,J),J=1,NPTS), I=1,NENS) 10 F0RMAT(32F4.4) C SET CONSTANTS AND ZERO APPROPRIATE ARRAYS TOT=FLOAT(NENS*NPTS) DFR=1./(NPTS*SMDS) DFLIM=2.*AN/WAVE DO 11 I=l,NPTS/2 ADATA(I,2)=0.0 ADATA(I,1)=(I-1)*DFR*1000. 11 CONTINUE SUMTOT=SUMTSQ=0.0 C CALCULATE MEAN AND VARIANCE FOR BLOCKS AND TOTAL DATA DO 12 M=1,NENS DO 13 N=1,NPTS C CONVERT FROM MICRO TO MACRO TRANSMISSION DATA(M,N)=10.**(-((-AL0G10(DATA(M,N)))*SMAMIC+CMAMIC-DMACB))

SUMTOT=DATA(M , N ) +SUMTOT SUMTSQ=SUMTSQ+(DATA(M,N)**2) 13 CONTINUE 12 CONTINUE TAV=SUMTOT/TOT TVAR= ( SUMTSQ /TOT ) - ( TAV**2 ) C CALCULATE % ERROR(TRABKA) FOR REFLECTION TO DENSITY CONVERSION TRABKA=(SQRT(TVAR))/TAV TYPE TRABKA TAV C CALCULATE REFLECTION TO DENSITY CONVERSION

DC=( .434294481903251/TAV)**2 C LOAD TRANSFORM ARRAY DO 14 J=1,NENS DO 15 K=1,NPTS 15 TRAN(K)=DATA(J,K)-TAV CALL F0URT(TRAN,200,1,-1,0,W0RK,5) 138

DO 16 L=1,NPTS,2 C=(TRAN(L)**2)+(TRAN(L+1)**2) 16 ADATA((L+l)/2,2)=ADATA((L+l)/2,2)+(C/FLOAT(NENS)) 14 CONTINUE DO 17 I=l,NPTS/2 17 ADATA(I,2)=ADATA(I,2)*EL*SMDS/NPTS*DC C MAKE CORRECTIONS FOR SLIT MTF AND OPTICS MTF DO 18 J=2,NPTS/2 U=(J-1)*DFR ARG=U*SLWI*PI SLCOR= ( ARG**2 ) / ( S I N ( ARG ) **2 )

ANCOR=( 1 .-(U*( 1 ./.8*DFLIM) ) )**2 CF=ANCOR/SLCOR ADATA(J,2)=ADATA(J,2)/CF IF(CF.LT..2) KTP=J GO TO 181 18 CONTINUE C DETERMINE CONFIDENCE LIMITS ON SPECTRUM FOR DGFR t 100 181 DGFR=NENS*2 CSUL=.5*((-1.96+S0RT(2.*DGFR-1.))**2) CSLL=.5*((1.96+SQRT(2.*DGFR-1.))**2) UV=DGFR/CSUL BV=DGFR/CSLL C OUTPUT DATA WRITE(116,19) (ADATA(K,1),ADATA(K,2)), K=1,KTP WRITE(116,19) WRITE(116,19) (ADATA(K,1),ADATA(K,2)*UV), K=1,KTP WRITE(116,19) WRITE(116,19) (ADATA(K,1),ADATA(K,2)*BV), K=1,KTP 19 FORMAT (2G4. 4) END 139

8. VITA

Born, raised, and educated in Lorain, Ohio, the author pursued his college education in Photographic Science and

Instrumentation at Rochester Institute of Technology. While a student at R.I.T. he was awarded the Fuji Photo Scholarship, along with serving as president of the joint student chapters of the Society for Photographic Scientists and Engineers, 4 Society of Motion Picture and Television Engineers. Gaining practical work experience through employment at the National Photographic Interpretation Center, and graduate assistantships at R.I.T., a working knowledge of photographic system physics was developed. This was further augmented through full -time work experience in image quality metrics, image structure modelling, microdensitometry, and digital image processing while employed at Xerox Corp. and Eastman Kodak Co.